Technically Monks can too, but their Zen Flight isn't nearly as useful as a replacement for flying mounts like Travel Form is.
Wait what the hell. How do I have a level 120 monk and never realised there's a flight form? I wonder how many other abilities I've missed on my priest and demon hunter.
I'm such a noob. Worst example: I didn't realise I was carrying a cursed coin on my main for 2 weeks that'd I'd picked up in Nazjatar. I wondered why I was dying so easily and then someone pointed it out to me when I was doing a dungeon.