Yes it's possible if one player holds AhK and one 8h9h and flop came down 10h Jh Qh then you have a royal flush and a straight flush. odds of it happening are pretty slim though.
Let's say I'm at the same table as you and I'm going to play with 89 diamond, you call with AK diamond, the board on the flop shows Diamond TJQ, so there's a possibility yes, answering your question. Good luck on the tables.
It is possible 8d-9d vs. Ad-Kd. Flop = 10d , Jd, Qd, blank, blank, that's a Royal Flush over a Straight Flush where both cards play.
This is what we call A BBJ . bad beat jackpot, casinos pay out a lump sum when hands like this hit. Both hole cards must play , Both hands must be tabled, and your chips can't be in racks to win . those are the rules at my casino.