The thrown weapon fighting style says:
You can draw a weapon that has the thrown property as part of the attack you make with the weapon. In addition, when you hit with a ranged attack using a thrown weapon, you gain a +2 bonus to the damage roll.
Boomerangs, listed here, and the Storm Boomerang which is not in SRD, don’t have the thrown property. This would seem to exclude them from the first ability which is very explicit about what it affects, and possibly exclude them from the second, depending whether "thrown weapon" refers to a weapon with the thrown property or to any weapon that is thrown to make a ranged attack. This seems absurd though.