Mildest rhymes with:
coldest, eldest, oldest, blondest, buddhist, coldest, eldest, encyclopedist, fondest, grandest, hardest, kindest, loudest, methodist, modest, oddest, oldest, orthopedist, prejudiced, propagandist, proudest, rudest, saddest, sadist, shrewdest, soundest, stupidest, weirdest, widest
Mildest sounds like:
maladjusted, malatesta, multistate