After I posted my response I re-read the date. I was confusing Peter Fleck's birth date (1788) with John's birth date (1780) maybe related but different line. I have another Fleck Bible and it lists a John Fleck born 1840. The parents are not listed.
Yes, it is the Conrad Fleck line. My family did the footwork on that line (their grandmother was Izora Fleck) and I made the connection to Conrad Fleck through the internet.
I can send to a scan of the bible page showing all the brothers and sisters.