I can't remember a specific time when it was mentioned in the series. IIRC, Clark flew (by plane) to California for that interview with the killer on death row (Lex Files, S4), and he never mentioned anything about problems with the flight.
I believe the dislike of flying grew out of the Never on Sunday episode in S3, when we learned that Clark is claustrophobic. Since Dean Cain also mentioned that he doesn't like flying (but I believe his is a fear-of-heights issue), some of the FoLCs may have applied his dislike to the character he played. However, Clark would be claustrophobic in any universe that had him arriving on earth as an infant in a tiny spacecraft.
Speaking as a claustrophobe, I don't get tense and nervous in elevators (plenty of room to move around and stretch out) or planes (same reasoning). What triggers mine is tight, dark places where I could reasonably (okay, unreasonably from an outsider's perspective
) get stuck. If I felt claustrophic on a plane, sitting in the cockpit where I had an almost unlimited view would quickly eliminate that feeling for me.
