If you are in Island of Blades stance do you and your allies lose your flanking bonus if you are invisible?
No, flanking is not affected by your visibility. For reference, we’ll go through the entirety of the flanking rules:
When making a melee attack, you get a +2 flanking bonus if your opponent is threatened by a character or creature friendly to you on the opponent’s opposite border or opposite corner.
When in doubt about whether two friendly characters flank an opponent in the middle, trace an imaginary line between the two friendly characters’ centers. If the line passes through opposite borders of the opponent’s space (including corners of those borders), then the opponent is flanked.
Exception: If a flanker takes up more than 1 square, it gets the flanking bonus if any square it occupies counts for flanking.
These first three paragraphs deal solely with positioning. Island of blades replaces these requirements wholesale with the following much simpler rule:
If both you and an ally are adjacent to the same creature, the two of you gain the benefit for flanking that opponent.
(Tome of Battle pg. 78)
There’s some more detail in Tome of Battle describing what happens with multiple allies or multiple enemies, but they don’t matter here; the short version is, it works.
Note that neither of these has anything to say about visibility; they are purely to do with positioning.
Only a creature or character that threatens the defender can help an attacker get a flanking bonus.
Being invisibile does not affect your ability to threaten the defender.
Creatures with a reach of 0 feet can’t flank an opponent.
Being invisible does not affect your reach in any way.
And that’s all of the flanking rules. There are no more to consider. Rules Compendium includes some handy diagrams, and a sidebar explaining how the flanking rules were developed, but also does not mention vision.
The invisibility rules are much longer, but the word “flank” does not appear anywhere in them (in fact, it appears nowhere in the entire Special Abilities page). Rules Compendium also discusses invisibility at length, and actually does update and change some of the rules, but again the word “flank” appears nowhere in it. The Vision and Light rules also make no mention of flanking (and again, “flank” appears nowhere in it, or anywhere else in the Exploration rules), and Rules Compendium doesn’t change any of those rules (though it does reorganize and move these rules around a lot and make it difficult to check).
One thing that should be mentioned, as it seems related: if the defender is not visible to you, then you cannot score critical hits against him or her. Since the main reason to care about flanking is Sneak Attack, and you cannot Sneak Attack what you can’t crit, this is a situation where invisibility can make flanking mostly pointless.