Inflames rhymes with:
flames, acclaim's, acclaims, blames, claims, disclaims, exclaims, flames, proclaims, acclaim's, acclaims, adames, aim's, aims, ames, ames', blames, claims, crames, dame's, dames, disclaims, exclaims, flames, frames, game's, games, games', grames, haimes, hames, haymes, james, james', jas, maims, name's, names, proclaims, rhames, same's, sames, shames, st-james, st_james, tames
Inflames sounds like:
imbalance, imbalances, impaling, implying, inflaming, influence, influences, influenza