The Australian pair's compatriots Maddison Keeney and Anabelle Smith, bronze medallists at the 2016 Rio Olympics, had led the competition until the last round but appeared to be affected by the delays and recorded a no-dive.
"It was all over the shop for everyone with all the delays and technical stuff going on," Kenney said. "I think it was an interesting day for everyone, I don't think anyone could say they dived well."
Sheehan and Qin had been three points outside the medals before they scored 71.10 with an inward 2-1/2 pike somersault on their fifth dive to finish with 284.10.
England's Alicia Blagg and Katherine Torrance finished second on 276.90, as Malaysian duo Mun-Yee Leong and Nur Dhabitah Sabri claimed bronze with 264.90.
Kenney and Smith finished seventh on 224.31 points as all the divers struggled with the tricky and chilly winds.
"It is disappointing because we've been training well with the little preparation we've had, but at the end of the day this isn't our major goal in the next four years, Tokyo is," Smith said.
"In a couple of weeks time we probably won't remember this."
(Reporting by Greg Stutchbury; Editing by John O'Brien)
