tl;dr: it depends on a few things but the chances of opponent having a better flush is somewhere in the 43% area if we assume villain opens from EP and its HU between you and villain. He'll also have you beat with a full house or quads ~6.7% of the time. He has a worse flush than you about 20% of the time.
I can't give you a clear cut answer for your exact situation because the information is missing from the question.
However, let's assume that villain is pretty solid and opening up with a hypothetical 15.4% range from early position; a range consisting of 55+, A4s, A6s+, ATo+, K8s+, KJo+, QTs, JTs, T9s. This is not a "GTO" range by any means but an example of a range that a relatively tight player might show up with.
We assume you flat the open from LP. Everyone else folds.
On the 6h9hQh flop villain has a flush 5.26% of the time, set 5.26% of the time, overpair 9.02% of the time along side a flush-draw 4.51% of the time and no flush draw 4.51% of the time. Villain also has top pair 15% of the time along side a flush-draw 3.01% of the time and no flush draw 12% of the time. Villain finally has ace high 38.5% of the time and no made hand 13.5% of the time. The total combos of flush draws result in a nut flush draw 10.5% of the time and 2nd nut flush draw 8.27% of the time. Villain eventually has a weak flush draw 11.3% of the time too on the flop.
This basically means that villain has the flush on the flop 5.26% of the time, the nut flush draw 10.5% of the time and the 2nd nut flush draw 8.27% of the time. Then villain has a weak flush-draw 11.3% of the time. Villain also flopped a flush 5.26% of the time, that's 7 combos. These 7 flush combos are all Ahxh or Khxh, meaning all flushes villain has on the flop are nut flushes.
The turn is the 9s. If we assume that villain bets top pair+, nut flush draws (18.9%), 2nd nut flush draws (14.9%) and weak flush-draws (20.3%) then he bets 56.5% of the time. Let's assume he does.
We then arrive by the river on the 2h. Using the previous filters, we can see that villain has quads 1.35% of the time, a full house 5.41% of the time, the nut flush 25.7% of the time, 2nd nut flush 17.6% of the time, an over pair 8.11% of the time, the 4th nut flush 8.11% of the time and a weak flush 12.2% of the time. You have the 3rd nut flush draw so villain can't have that.
To sum up an answer: vs a semi-tight open, a flop barrel consisting of strong hands and flush draws, a turn barrel consisting of strong hands and flush-draws, then villain will have a worse flush than you roughly 20.31% of the time.
This is not a perfect analysis since its making assumptions that may or may not be correct, but it gives you an idea. Even vs a relatively wider range you should not expect to see this get much better, while villain might have a few more combos of worse flushes he would have more combos of nut flushes and second nut flushes at the same time so it should be be in the 20% area.
You can use FlopZilla for this street by street analysis, where you can put in a range you think fits villain better, place filters on which cards you think villain gets to the next street with and of course this takes your hand into account which blocks the hands villain can have. I hope this somewhat helps!
