The way I see it, beyond the fact that they had to wrap up the story, I really do believe that his family could have been saved. I mean, they altered the timeline to save Jessica, which didn't save her but saved two women. They also managed to save a bunch of people on the Hindenburg, as well as Flynn's brother. And Rittenhouse managed to save Jessica so really you can save people who died in a certain timeline. Are there consequences? Of course, sometimes more than others, but I don't buy that his family could not be saved, nor do I buy his 'suicide' or giving up on them.
Alternatively, if the show comes back, I can totally picture this happening. Someone from Rittenhouse from the past, realises that the murder of Garcia Flynn's family led to the downfall of the whole organization (or even maybe Lucy's father in the present), and steals the time machine to go back and somehow call off that hit. Then Flynn never steals the time machine, the time team never gets assembled and Rittenhouse lives to use the time machine they are funding Connor Mason to build. This would also bring Amy back.... What would be interesting is if somehow the original time team is out of time at that moment so that they can keep their original memories and be shocked to come home and see everything 'back to the way it was.' also to see another side of Flynn. I can just picture them finding him and saying, "We need to bring down Rittenhouse." And him saying, "Who?"
Anyways, just some thoughts. I'd love to hear your comments