I am looking for a book I read in Jr. High/High School in the late 80s to early 90s. It had to do with a dragon and his rider, a young teenage boy, who could time travel while in flight.
Sorry I can't provide more clues... It's been almost 30 yrs.
This is one or more of the novels in Anne McCaffrey's Dragonriders of Pern series, which began in 1967. The characters in these novels can travel through time while riding their dragons.
The original three novels were Dragonflight, Dragonquest, and The White Dragon.
You most likely read The White Dragon, which concerns the story of Jaxom, a young lord, and his dragon Ruth.
You could also be thinking about Riftwar Saga by Raymond Feist. One of the characters becomes a dragon rider and has some ability to move differently through space and time. These abilities come into full force in the last two books, particularly A Darkness at Sethanon.
Edit: This wiki page gives a reasonable summary of the character's story arc. (Spoilers if you haven't read the books, of course.) http://midkemia.wikia.com/wiki/Tomas_Megarson