In my exhausting search for one mere move I have learned at least one thing.
That some moves are rarer than others, some by a slight margin, and a select few by a landslide. I have been searching non-stop for months trying to find Blast Burn on a Charizard and have not succeded yet. The ways I know with little doubt that Blast Burn is 1. In the game and 2. able to be learned by Charizard is that I have a Feraligatr with Hydro Cannon and I checked to see if a Blastoice could learn it at the move school and it could.
I have found numerous (let's say at least 7) Charizards with Belly Drum- an at least rare move. I also collected data on a Charizard I repeatedly rusty reset that never had Blast Burn. I'll update this page with the data for that and around how many Charizards I have befriended looking for Blast Burn Soon. Anyways, I have concluded that the three best moves of their type (elemental hyper beams, Frenzy Plant, Blast Burn, and Hydro Cannon) are the rarest moves in the game. I wish there could be technical data on move rarities but the best that can be done (besides hacking which I really wish someone would do already) is to experimentally determine them.
I am also aware of other rare moves that non-legendaries can know (like Belly Drum and D Dance) and also legendary exclusive ones (like Blue Flare and Bolt Strike). I also know that Bolt Strike is rarer than Fusion Bolt and Blue Flare is rarer than Fusion Flare. I'm sure there are at least a few legendaries that know more than one exclusive move like that that is rarer but I cannot think of any at the moment.
I forgot exactly how rare Hydro Cannon was on my Feraligatr but I know it had to have taken a while. If anyone has Blast Burn or Frenzy plant I would love to see pics or a video of them in action.