@tanguatlay,
The phrase ‘more than my fair share,’ is used to express that someone has seen a lot of or done a lot of something. Quite often it’s something arduousorunpleasant.
A fireman could say they’d seen more than their fair share of house fires, or a homicide detective could say they’d seen more than their fair share of murder victims.
I suspect that is what the writer means to say, that they have seen a lot of road accidents in their time, probably even more than most people. However, as they’ve missed out more it simply means they had seen as many accidents as one would expect someone of their age to have seen.