Flitting rhymes with:
slitting, splitting, acquitting, admitting, befitting, bitting, committing, emitting, fitting, gritting, hitting, knitting, omitting, permitting, pitting, quitting, refitting, resubmitting, sitting, slitting, spitting, splitting, submitting, transmitting, unremitting, unwitting, whitting, witting
Flitting sounds like:
faulding, faulting, feldman's, fielding, flatness, flattening, fleeting, floating, flooding, flouting, folding, fulton's