The left-handed Flynn will be making his second start since being a September callup from Triple-A New Orleans.
In his Major League debut on Sept. 4 against the Cubs at Wrigley Field, Flynn had a no-decision.
Turner, who has struggled in the second half, will be given a couple of extra days to help get back on track. With Flynn now set for Friday, Turner will pitch the series finale on Sunday at New York.
Flynn will stay in the rotation, filling in the spot vacated when Jose Fernandez is shut down after his Wednesday start.
"Flynn will take over for Jose when he filters out of the rotation," manager Mike Redmond said. "We've set things up pretty much until the end of the season."
On Saturday at New York, the Marlins will play a doubleheader. Henderson Alvarez will pitch the first game, and Brad Hand will go in the second game.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter