Synonyms for Kick in:

n.

bring out, take effect, interact, shape, impact, come into play, get, make a difference, affect, put. equip, supply, resource, serve, provide, cater to, offer, come up with, arrange, satisfy. set about, kick out, kick/beat the shit out of someone, kick someone's face/teeth/head in, boot, put/stick the boot in, fight back. contribute (noun)
donate.
kick in (noun)
chip in, set in, kick down, give, contribute.

v.

contribute (verb)
chip in, donate, give, provide.
stative (verb)
set in.

Other synonyms:

donate. supply
cater to.
Other relevant words:
contribute, donate, provide, supply.