The Marlins held out hope Eovaldi would be better, but when there was little improvement, the club went to their backup plan. Flynn, a September callup, was lined up to go on Friday against the Mets at Citi Field.
The revised rotation now has Brad Hand facing the Mets on Friday, and Henderson Alvarez will pitch the first game of Saturday's doubleheader, followed by Jacob Turner. Tom Koehler will pitch Sunday.
Eovaldi opened the season on the disabled list with right shoulder inflammation and joined the rotation in June.
"His back is really tight," manager Mike Redmond said. "He's not really moving well."
Sam Dyson is a candidate to go on Monday in Philadelphia, if Eovaldi isn't ready.
The Marlins are confident Eovaldi will pitch again this season, but they also are being careful with the hard-throwing right-hander.
"I'm anticipating him pitching at least one more game," Redmond said. "It depends on the timing on how long he is going to be out. With all these guys, we've got to make sure we take care of him. We don't want to jeopardize his arm after missing time with a sore shoulder. We have to make sure he's back healthy and feeling good before we send him back out there."