Dukedom rhymes with:
sheikdom, adam, addendum, afrikanerdom, boredom, cadam, carborundum, chiefdom, christendom, condom, corundum, dedham, earldom, edam, fiefdom, fordham, freedom, gaddum, hildum, kingdom, leedom, macadam, madam, madame, martyrdom, mcadam, memorandum, modem, needham, nydam, odom, odum, officialdom, oldham, purdham, purdom, purdum, random, referendum, rodham, saddam, sandom, sedam, sedum, seldom, sheikdom, sodom, stardom, subkingdom, suydam, tandem, windham, windom, wisdom, wyndham
Dukedom sounds like:
d'agostino, dagestan, dagostino, dakotan, daughton, dedication, deduction, degaetano, deighton, desiccation, destin, destiny, destitution, detection, detoxication, dichotomy, dickstein, dictation, diction, dictum, dideoxycytidine, digaetano, digestion, digidyne, disdain, dissection, dissociation, doughten, dustin, dustman, duston