Can Forge of the Future kill this be played at reaction speed

No — "Kill this" is an activated ability with Main Phase timing, and Forge of the Future lacks Reaction, so it can't be played at reaction speed.

Gear activated abilities ([Cost]: [Effect], see the colon) can only be activated during your own Main Phase, in an Open State, and never during a Showdown (Rules 150.2, 151.2). Reaction is a permissive keyword that grants Closed State/opponent's-turn timing (Rule 813) — Forge doesn't have it, so the ability can only be used in a neutral open state on your turn, and it can't respond to anything already on the Chain (FAQ #8888).