Not Netflix, but PBS, so it may be available to most: Once Upon a Time in Space.
I had set my EweTubeTV to record the show, and just watched the first episode (and only two are out, must be a new show). Brief prelude about the start of the US Space program, but it looks like the main subject is the Space Shuttle program, and it concentrates less on the tech aspects and more on the race/sex/skillset/political aspects of things (the US astronauts up to that point were white, male, AF pilots). Lots of interviews with the old astronauts, their wives and children, and lots of 8mm home video footage. The first episode ended with the Challenger disaster.
This is especially interesting to me as I was hired two years later by Thiokol, the builder of the Space Shuttle's boosters (whose segment joint design caused the explosion). Two years after that I went back to USAF engineering, but was very thankful for my couple years working with NASA and for Thiokol.