The Two-Weapon Fighting feat by base definition gives bonuses to negate the usual penalties of dual wielding. Does this have any effect on a monk's Flurry of Blows ability, where the penalties disappear completely after two levels?
No, no feat of the TWF tree helps negate the bonuses from monks flurry of blows. However, remember that Two Weapon Fighting can be used together with the flurry, although one has to be careful not to stack too many penalties.
Also, saying that the TWF feat gives bonuses is a rather liberal interpretation:
Your penalties on attack rolls for fighting with two weapons are reduced. The penalty for your primary hand lessens by 2 and the one for your off hand lessens by 6. See the Two-Weapon Fighting special attack.
This doesn't in any way suggest bonuses that counterweight the penalties -- it simply reduces the penalties, "modifying the penalty rules", you could say, in your case.
Two-Weapon Fighting does not reduce the penalties from Flurry of Blows, since Flurry is not the same thing as fighting with two weapons:
The only thing Two-Weapon Fighting and Flurry have in common are that they grant an extra attack. The Two-Weapon Fighting feat only reduces the -6/-10 penalties for fighting with a second weapon in your off-hand, but even with flurry a monk using unarmed strikes has no off-hand. All his unarmed strikes are considered on-hand.
Interestingly, according to the D&D 3.5 FAQ, a monk can use Two-Weapon Fighting to make an extra off-hand attack, even on top of Flurry, but the penalties from Two-Weapon Fighting stack the penalties from Flurry:
In other words, a first-level monk with the Two-Weapon Fighting feat has four options: make one attack at +0, Flurry for two attacks at -2/-2, TWF for two attacks at -2/-2 (but one of those is off-hand and applies only half Strength modifier), or combine Flurry and TWF for three attacks at -4/-4/-4 with one of those an off-hand attack. You can't use the Two-Weapon Fighting feat on its own to reduce Flurry's penalties.