By default, no.
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.
You only get this bonus if you are flanking with a partner on the opposite side: if two allies flank the target and you are coming from a different angle (without a partner), the target is not “threatened by a character or creature friendly to you on the opponent’s opposite border or opposite corner,” so you do not get a flanking bonus. The fact that your allies are flanking the target (and do get that bonus when they attack themselves) is not relevant at all.
The rogue’s attack deals extra damage any time [...] when the rogue flanks her target.
(Sneak attack rules)
This specifies that the rogue must be flanking the target, rather than the target merely be flanked. Note how this contrasts with the other option, “any time her target would be denied a Dexterity bonus to AC,” which only cares that the target is in that state, not how it came to be or whether the rogue caused it. The subject of the denied-Dex condition is the target itself, while the subject of the flanking condition is the rogue.
However, there are ways to work around this.
The easiest and most effective is probably island of blades, a Shadow Hand stance from Tome of Battle. While in this stance, you and your allies flank merely by both being adjacent to a target, rather than having to be on opposite sides of the target. That would allow the rogue here to be flanking, gaining its intrinsic bonus as well as enabling sneak attack. In fact, island of blades would allow the rogue to flank and sneak attack with just one of the warriors, and also lets that warrior also flank.
A rogue can pick up island of blades as early as 3rd level by taking the Martial Study feat for any Shadow Hand maneuver at 1st, and then the Martial Stance feat at 3rd to pick up island of blades. Both Martial Study and Martial Stance are feats in Tome of Battle itself. Alternatively, the swordsage base class from the same can get island of blades as a 1st-level class feature, making that an attractive multiclass option for a rogue. Having a Shadow Hand stance also enables the use of the excellent Shadow Blade feat, allowing you to use Dexterity instead of Strength to your damage with certain weapons—most rogues will appreciate that.
Other, similar effects exist; it seems beyond the scope of this question to attempt to list them all here.