There are multiple Tina Turner documentaries, but only one is currently streaming. That's 2021's TINA, a hit with both critics and viewers (92% on Rotten Tomatoes, with a 91% audience score).
TINA, from directors Dan Lindsay and T.J. Martin, unearthed never-before seen footage and interviews (including with Ms. Turner herself for this film. It also shows how she struggled to live her life when her story was out of her control.
Tina is streaming on Max (the new HBO Max)