If you have too many accidents that are 100 percent NOT your fault you can get fired because insurance still thinks you're a risk.
They'll most likely look at it from a dollar perspective (no pun intended). Seems like your mishaps have been low cost so you should be fine, same from when applying with future employers. It's major screws up like rear ending ppl, running over puppies and blind ladies that are completely unacceptable
If the first accident wasn't your fault get the police report as mentioned earlier. As far as bending a rim and flattening a tire I don't see that as an offense for termination. Don't give up if it's what you really want to do.