Scotland host Denmark and Moldova, and are away to Austria.
Centre-back Cooper had a light pre-season in terms of minutes on the field having appeared at Euro 2020 but has played the whole of both Premier League matches since the new season kicked off. Midfielder Fleck has started three of the Blades' four Championship games.
There are first call-ups for St Johnstone goalkeeper Zander Clark and Aberdeen midfielder Lewis Ferguson, but no place for Manchester United's Scott McTominay, who is injured.
Motherwell goalkeeper Liam Kelly is also uncapped but unlike Clark and Ferguson, has been in the squad before. Former Bradford City and Harrogate Town goalkeeper Jon McLaughlin is another who has lost his place since the European Championship, where Scotland failed to qualify from a group which also featured England.
Meanwhile manager Steve Clarke has signed a contract extension until 2024.
Goalkeepers: Zander Clark (St Johnstone), Craig Gordon (Hearts), Liam Kelly (Motherwell)
Defenders: Liam Cooper (Leeds), Declan Gallagher (Aberdeen), Grant Hanley (Norwich), Jack Hendry (Oostende), Scott McKenna (Nottingham Forest), Nathan Patterson (Rangers), Andy Robertson (Liverpool), Greg Taylor (Celtic), Kieran Tierney (Arsenal)
Midfielders: Stuart Armstrong (Southampton), Lewis Ferguson (Aberdeen), Billy Gilmour (Chelsea), John McGinn (Aston Villa), Callum McGregor (Celtic), Kenny McLean (Norwich City), David Turnbull (Celtic)
Attackers: Che Adams (Southampton), Ryan Christie (Celtic), Lyndon Dykes (QPR), James Forrest (Celtic), Ryan Fraser (Newcastle), Kevin Nisbet (Hibs)