Final Crisis: Rage of the Red Lanterns #1 doesn’t really have anything to do with the actual Final Crisis event and I suggest reading it after the event as part of the lead up to Blackest Night.  If you want to read it as part of this order read it after Final Crisis #1.

Justice League of America Vol. 2 #21

Final Crisis #1 (2008)

Final Crisis: Requiem #1 (2008)

Final Crisis #2

Final Crisis: Rogues’ Revenge #1 (2008)
Final Crisis: Rogues’ Revenge #2
Final Crisis: Rogues’ Revenge #3

Final Crisis #3

Final Crisis: Superman Beyond #1 (2008)
Final Crisis: Superman Beyond #2

Final Crisis: Legion of 3 Worlds #1 (2008)
Final Crisis: Legion of 3 Worlds #2
Final Crisis: Legion of 3 Worlds #3
Final Crisis: Legion of 3 Worlds #4
Final Crisis: Legion of 3 Worlds #5

Final Crisis: Revelations #1 (2008)
Final Crisis: Revelations #2
Final Crisis: Revelations #3
Final Crisis: Revelations #4
Final Crisis: Revelations #5

Final Crisis: Secret Files #1 (2009)

Final Crisis: Resist #1 (2008)

Final Crisis: Submit #1 (2008)

Final Crisis #4
Final Crisis #5

Batman #682
Batman #683

Final Crisis #6
Final Crisis #7

Superman/Batman #76