So with elemental trap, it says that you can't use gather power to reduce the burn for the optional, but it doesn't say that your other ability, infusion specialization, can't reduce the burn.
Is there any reason raw it wouldn't?
Infusion specialization has a short description with little ambiguity (unlike most kineticist rules) and by RAW would reduce the burn. I suspect RAI would be different but there's no proof.