Fan clubs mostly come up with those. Quite often on roadtrips. Long bus rides give plenty of time to think of chants and practice them. It also helps that fan clubs typically go to games as big groups instead of being scattered all around, and they also go to every game.
It likely wouldn't take THAT much to start organizing something like that in Calgary.
Get some fans together, find a place where you can meet and drink, start thinking of chants, steal some existing chants or make them your own, accept that you'll be lucky to come up with any good ones to begin with, then practice the best chants by yourselves. (You WILL need to drink to do that
)
When you got a couple, then you go to games to try and get them going. It will take some organizing, and it might take some time to get other people to join in (as in, several games), but the reward is feeling like a legend and possibly becoming a part of Flames tradition.
Once you have some, you can also try recording them and posting them on CP.