"Flyers" doesn't work for Philadelphia, "Flames" doesn't work for Atlanta or Calgary, "Jets" doesn't work for Winnipeg, "Devils" doesn't work for New Jersey, neither "Ducks" nor "Mighty Ducks" work for Anaheim.
No, that doesn't make sense. The standard on the site is that Flames should work for both teams. If you're going to let one team be guessed with the nickname and force full spelling of the other, which one gets the nickname? You've chosen Calgary, presumably because they had it most recently. I think it should be Atlanta, since they had it first. "Flames" should just work for both teams.
It's not really correct to list the Arenas, St. Patricks, and Maple Leafs as though they were different teams, or the Cougars, Falcons, and Red Wings as different teams. I agree that a move makes it a different team. If you're going to make a simple name change count as a different team, then you need to split up California Golden Seals from 1967-1976 into:
California Seals (1967)
Oakland Seals (1967-1970)
Bay Area Seals (1970)
California Golden Seals (1970-1976)
Also, now you have the problem that "Seals" can't work for all four "teams" (according to your policy on "Flames" for Atlanta and Calgary), so you'll have to type "Seals" for the Bay Area Seals, "California Seals", "Oakland Seals", and "California Golden Seals" to get all four.
California Seals (1967)
Oakland Seals (1967-1970)
Bay Area Seals (1970)
California Golden Seals (1970-1976)
Also, now you have the problem that "Seals" can't work for all four "teams" (according to your policy on "Flames" for Atlanta and Calgary), so you'll have to type "Seals" for the Bay Area Seals, "California Seals", "Oakland Seals", and "California Golden Seals" to get all four.