Jack Flaherty trade idea No. 1) Dodgers
Jack is originally from the Los Angeles area and went to high school there. While he has said in the past that he wants to stay in St. Louis, I'm sure he would love a return to his home town. Also, the Dodgers wouldn't complain about receiving a pitcher who would slot in just behind Julio Urias, Clayton Kershaw, and Tony Gonsolin.
Flaherty would provide high upside for a team with annual World Series aspirations. He could easily start a playoff game and pitch into the 7th inning. The Dodgers would more than likely want a strong reliever as well. Their organization does a good job of using pitchers late in games, and the Cardinals have some relivers who could also be shipped off.
The Dodgers have a fantastic farm system. It is unrealistic to expect two top-three prospects in return, let alone one. However, the Dodgers do have a high-end pitcher in their farm system that may be appealing and achievable to the Cardinals: Gavin Stone. If paired with a strong reliever, Flaherty could bring back the Dodgers' fourth-ranked prospect (seventh best right-handed pitching prospect in MLB).
Currently, Gavin Stone is pitching for Triple-A Oklahoma City for the Dodgers. He has a 5.86 ERA, 1.486 WHIP, and has accrued 82 strikeouts in 70-2/3 innings. MLB.com states that "While Stone is less physical than desired for a starter, he's athletic and has an efficient delivery that helps him hold his stuff and provides consistent strikes". Stone is ranked #48 by MLB.com for all prospects.
The Dodgers would also have to include a throw-in prospect. Nick Nastrini seems to fit the bill. He's a high-K, high-BB guy with some upside as a starter but more upside as a reliever. The Cardinals can take a flier on him while the Dodgers are willing to let him go as they have ample pitchers in the minors.