Thicker rhymes with:
bicker, bricker, clicker, dicker, ficker, flicker, fricker, kicker, knicker, licker, liquor, macvicar, mcvicar, mcvicker, picker, quicker, redicker, ricker, schicker, schlicher, schlicker, schricker, sicker, slicker, snicker, sticker, stricker, ticker, vicar, vicker, whicker, wicker, zwicker, zycher
Thicker sounds like:
tacker, tager, takara, takecare, taker, taser, tashiro, tasker, taucher, tauscher, taxer, teacher, teaser, teicher, teixeira, tejera, tesar, tesoriero, tesoro, tessier, teuscher, texeira, thacher, thacker, thackeray, thakkar, thaser, thatcher, thuggery, ticer, ticker, ticor, tigar, tiger, tigera, tischer, tisher, titzer, tokar, tooker, toothaker, toshiharu, tougher, tozer, tozier, tsar, tucker, tweezer, tygar, tyger