Scenario 1: "When my allies are flanking a foe, if I threaten that foe then I count as flanking that foe"
First, you can (but don't have to) remove either one (but not both) of your allies from the diagram and still be counted as flanking that foe by employing the following feats:
The style feat Despana School (Drow of the Underdark 56), in addition to other benefits, allows you to remove either ally from the diagram and still leave you and the other ally flanking the foe if that other ally is a monster that you summoned. The feat doesn't require adjacency, so with this feat you're also flanking in scenario 3 as long as either ally is a monster that you summoned; this, too, renders the other ally irrelevant for flanking purposes and also eliminates scenario 3's need for the need for stance island of blades (Tome of Battle 37). The Despana School feat's prerequisite is a base attack bonus of +5, the ability to cast a summon monster spell, and the feats Power Attack (Player's Handbook 98) and Weapon Focus (PH 102), with the latter applied to either the light mace, heave mace, or warmace (Dungeon #133 80 superseding Complete Warrior 154, 158) (25 gp; 10 lbs.). You were building around this, right?
The general feat that's also a fighter bonus feat Double Team (Dragon Compendium Volume 1 95—6 and not to be confused with the totally different feat of the same name from the earlier Dragon #357 39) allows you to remove either ally from the diagram and still leave you and the ally flanking the foe if both you and that ally have this feat. This feat also doesn't require adjacency, so in scenario 3 you're also flanking if both you and either ally have this feat; in scenario 3, again, the other ally is rendered irrelevant for flanking purposes and the island of blades stance remains unnecessary. The Double Team feat's prerequisite is an excessive base attack bonus of +6 and the feat Combat Reflexes (Player's Handbook 92).
If any route in this answer can be recommended, it's probably this feat. The 2nd-level Sor/Wiz spell heroics [trans] (Spell Compendium 113) can grant the feat to folks who meet its prerequisite so they don't have to actually take it. Heck, if the party has the heroics spell available, you don't have to take the Double Team feat. It's not like it's a prerequisite for anything.
The Rokugan ancestor (Crab) feat Great Teamwork (Oriental Adventures 63) allows you to remove either ally from the diagram and still leave you and the ally flanking the foe, but this benefit only applies while you're adjacent, so it does not also apply to scenario 3. Note that "[a]ny character can choose an ancestor feat, but only at 1st level" (Dragon #318 37), and the feat otherwise has no prerequisite. A similar benefit is realized from the feat Adaptable Flanker (Player's Handbook II 71, 74), but its prerequisite is ridiculous and its benefit inferior.
Now, with that out of the way, so far as I'm aware, only one official Dungeons & Dragons 3.5 game element facilitates flanking in the way that's actually desired in scenario 1: the teamwork benefit superior flank (Dungeon Master's Guide II 194).
Acquiring teamwork benefits
Because they're pretty obscure, here's the skinny on teamwork benefits: To acquire a teamwork benefit (Dungeon Master's Guide II 189—90) the team leader must have at least 4 Hit Dice, have at least an Intelligence score of 3, must be able to communicate with other members of the team, and meet the teamwork benefit's leader prerequisite, and each team member must have at least 4 Hit Dice, have at least an Intelligence score of 3, and meet the teamwork benefit's team member prerequisite. Then the team of 2—8 members (including the leader) trains together for 2 weeks, and one or more teamwork benefits are gained (up to 1 per 4 HD of the lowest-HD team member). Four times per year for 1 week each time, the team must again train together or else teamwork benefits are lost.
However, teamwork benefits just take time—no money need be spent to get teamwork benefits. Further, the design is fairly smart: the entire team need not be present for a teamwork benefit to be realized. If Jake's PC is the team leader or a team member and Jake's PC is dead, in prison, or off terrorizing peasants, then the rest of the team can go adventuring and still realize teamwork benefits (at least until it comes time to maintain the teamwork benefit).
Also, explicitly allowed to be team members are animal companions, familiars, and special mounts, but, of course, of course, they must still meet any benefit's prerequisite.
For all this time and trouble, the teamwork benefit superior flank grants the following as its primary benefit:
Whenever two members of your team flank the same enemy, all members of the team can make melee attacks against that enemy as if they also flanked her. Creatures that can’t be flanked are unaffected.
Hence the teamwork ability superior flank only works with specific allies, but it does the thing that's desired in scenario 1 and your ally doesn't have to be a summoned monster or waste a feat to hang out with you, and you don't have to be from Rokugan. As an added incentive, every member of the team can do what you wanted to do, too. The team leader prerequisite for superior flank is sneak attack +4d6, and the team member prerequisite is base attack bonus +3.
Scenario 2: "When my allies are flanking a foe, I count as flanking that foe with a ranged weapon."
Nothing does this directly. However, as a curiosity, the whisperknife prestige class's level 9 extraordinary ability ranged flank says
At 9th level, you know how to flank a foe by using a ranged weapon. You must be within 10 feet of the enemy in question, and you flank as if you were wielding a reach weapon…. You do not threaten the foe and may not make attacks of opportunity against the foe unless you are actually adjacent to the foe and armed with a melee weapon. (Races of the Wild 136)
Got that? Okay. Scoot 5 ft. to the right. There. Good. Now, if you're a level 9 whisperknife—and I'm not judging you—, then you're kind of in scenario 3 instead. Good luck.
Scenario 3: "If my allies or I possess an exceptional ability, I count as flanking that foe with a reach weapon."
Scenario 1 already describes the Despana School and Double Team feats. They do this. There aren't further exceptions that I'm aware of.
Scenario X: "If I've got the monster's nose, my allies count as flanking that foe" and other unusual options
These are additional options that I thought might be of interest despite not meeting the above criteria.
The general feat and also fighter bonus feat Dedicated Nuisance (Dragon #343 93) allows you to make a melee touch that, if successful, "[u]ntil just before your next turn, all creatures adjacent to the target other than yourself are considered to be flanking the target." This benefit is mind-affecting so you can't play I've Got Your Nose with vampires or whatever. Ask the DM if this melee touch attack must be made exclusively to activate the feat or if it can be any ol' melee touch attack. (I suspect it should probably be the former, but I think the latter's at least balanced.) Note that you must still conventionally flank a foe whose nose you stole if you want to flank that foe; this feat only helps your allies. The Dedicated Nuisance feat's ridiculous prerequisite is an Intelligence score of 13, a base attack bonus of +4, and the feat Combat Expertise (Player's Handbook 92).
The tactical feat Clarion Commander (Tome of Battle 34) allows you to use the tactical maneuver perpetual flank that says
To use this option, you make a DC 20 Intimidate check against an opponent as a standard action. If this check succeeds and you make a successful melee attack against the same foe on your next turn, you and your allies can treat that enemy as flanked for 1 minute.
In all but the most unusual encounters, successfully executing this tactical maneuver means that its benefit lasts until that encounter ends. The standard action that's required for the setup is an extremely high price, though, and a foe can foil your attempt in a variety of ways even before you miss with next turn's attacks, but if you can pull it off then the tactical maneuver perpetual flank may turn the tide of the battle for the right group—like a band of rogues, for example. The Clarion Commander feat's prerequisite is a base attack bonus of +6, two White Raven maneuvers, and the feat White Raven Defense (33–4) that itself requires a White Raven stance.
If both you and an ally have the technique (ronin) feat Serpent's Coil (Way of the Thief 47) and you and that ally flank the same foe, until the two of you aren't flanking that foe, that foe loses its Dexterity bonus to Armor Class. No, you're not misreading, and welcome to AEG's Oriental Adventures line. The foe loses its Dexterity bonus to AC against everyone and against every attack. You and your allies can even still get in there and flank that foe, too, if you want. If your other allies specifically need flanking, though, this is no help, but in the majority of cases—and, let's be honest, like you said, that's dealing sneak attack damage—, this is as good as flanking if not better.
Although the Serpent's Coil feat's prerequisite is only a base attack bonus of +4, that your allies also have to take it makes the actual price much higher. Even a DM who allows material from Way of the Thief may balk at allowing an animal companion or similar buddy to take the feat: the creature that takes the feat is supposed to be associated with the Serpents of Sanada organization described therein. Maybe they'll let your animal companion join? You can explain how he's a team player.
Note: This answer is for Dungeons & Dragons 3.5 exclusively and is not meant to be comprehensive. The writer has deliberately ignored Pathfinder material.