It seems to be a commonly accepted theory that the car skidded before going back to 1855. However, the car didn't really seem to skid, so much as explode. It certainly didn't appear to move in such a way that could possibly make those fire skid marks.
That said, I have a feeling the writers intended for the number 99 to be a way to pay tribute to some important event.
It might be possible that perhaps this was a tribute to Jules Verne. Michael Strogoff was publish 99 years before the movie was released. Dr. Brown's son, Jules, was also according to FuturePedia born 99 years before the first film began (Jules had a brother named Verne). However, I can't help but wonder why Back To The Future would have a reference to a book that itself wasn't even a science fiction.
Or, perhaps that was the speed the doc was moving (I guessing the faster you go, the harder it is to control the time in which the Flux Capacitor will send you, which could explain why Doc was sent to the old west). But, I can't imagine the speed would appear in backward flames like that.
Does anyone have a more solid theory?