The chance of the Flames or any team moving to Hamilton, or even a new team for that matter coming to Hamilton is exactly negative 140 percent.
The first issue is the competition, the Leafs and the Sabres are both against a Hamilton team as they fear it would impact their margins and that is an almost certain fact.
The comparisons made of Los Angeles and New York are ridiculous - Greater LA has a population of what, 18 or 19 million, and GLA probably excludes another million or so from the surrounding markets, greater NYC is over 20 million, compare that to the GTHA which is 7 million but excludes probably 1 million or so from surrounding markets and you can see the comparisons given are bunk.
The second issue is that Hamilton is inherently not a hockey town - a number of years ago, probably close to eight or ten the Bulldogs AHL team was sold off to somewhere else (cannot remember off the top of my head where exactly) and replaced by an OHL team of the same name. There has never been an enthusiasm around hockey or our team here; that is unlikely to change.
The third issue is the arena - FirstOntario centre was originally built with the faint hope that Hamilton could one day host an NHL team here (civic blowhards have deluded themselves for many decades over this “possibility”) but it is now old and shitty and awful. Because it is old and shitty and awful the City has now signed a deal (behind closed doors with zero competitive processes) with one of the bigwig event operator companies (Carmen’s partnership) here to renovate it, make them the operator of it (and develop some of the properties around it because this whole thing is a fucking taxpayer-funded private enrichment program for Carmen’s and their owners, the Mercanti’s), and part of that renovation will be downscaling the arena.
The fourth issue is Hamilton has at least three or maybe four teams now using that one arena - the Bulldogs, the Hamilton Honey Badgers basketball, and most recently the Toronto Rock Lacrosse team (who were basically priced out of Toronto, and then immediately offended Hamilton by refusing to change their name (and Hamilton has a huge rivalry with Toronto on apparently everything for some reason)) and there isn’t really any more space or time for another team. The FirstOntario Centre is also used for the largest events and often acts as a secondary Toronto arena - a few years ago BTS or Pinkblack or one of those K-POP groups came here and it was a goddamn mob scene.
In sum, it isn’t happening. I would be less surprised to see Hamilton become the home of Canada’s only NFL team because of a) how much more enthusiasm this city has for football and b) Toronto would be a no-go for NFL because the rest of the country has a similar hate-on for it and would never rally behind a Toronto team as a Canadian team.