Pickett's rhymes with:
rickets, ricketts, aftermarkets, checketts, euromarkets, haymarkets, hypermarkets, jackets, junkets, lockets, markets', nantucket's, packets, racquets, rickets, ricketts, supermarkets
Pickett's sounds like:
packets, packwood's, pact's, pacts, pagoda's, pagodas, pas-de-deux, pastas, pastes, pastiche, pastiches, pasts, pectic, pesetas, pestka, pests, phagocytes, physicists, piaget's, pickets, picts, pistachio, pistachios, pockets, posits, post's, post-attack, postage, postdates, posts, psychotic, pussycats