The Atlanta Flames moved to Calgary because the owner was losing money hand over fist in Atlanta, and the highest bids from prospective owners came from two groups who wanted to move the team to Calgary.
This article claims Cousins' ownership group had lost $1.7 million in '78-'79 and $2.8 million in '79-'80. That doesn't sound like a lot now but it was a lot then.
The Atlanta ownership group went as far as to monkey with the team's corporate structure in order to eke out some savings from a tax dodge:
http://news.google.com/newspapers?id=jMYvAAAAIBAJ&sjid=yjIDAAAAIBAJ&pg=3578,690839,
http://news.google.com/newspapers?id=HnVkAAAAIBAJ&sjid=MX4NAAAAIBAJ&pg=4140,2697803
U.S. Olympic hero Jim Craig joined the Flames immediately after winning the gold medal and had this to say about the fan support in Atlanta:
http://news.google.com/newspapers?id=Ei1eAAAAIBAJ&sjid=kV8NAAAAIBAJ&pg=4610,4088010
Actor Glenn Ford offered around $8 million to buy the team and keep it in Atlanta while the Seaman brothers (Byron, Donald and Doc) offered $14 million and were intent on moving the team to Calgary. In the end Nelson Skalbania (former co-owner of the Oilers and Indianapolis Racers; the man who signed Wayne Gretzky to his first pro contract and sold it to the Oilers for a pittance) offered $16 million, with the intent to move the team to Calgary, to which Cousins accepted. Skalbania almost immediately sold a portion of the team to Byron and Doc Seaman, Ralph Scurfield, Normie Kwong, Norm Green and Harley Hotchkiss. The rest of the owners didn't want to do ongoing business with Skalbania (who had a reputation as a bit of a shyster) and bought out Skalbania's share soon after.
I've read posts from many people here asserting that Cousins was losing money on his real estate developments and that's what precipitated the sale but every contemporary report of the time said the team itself was bleeding money. I am wont to believe in conspiracy theories about Cousins's real estate misadventures and supposed discovery of improprieties between the NHL Board of Governors (to which Cousins belonged anyway!) and the NHLPA executive (read: Alan Eagleson) being the driving factors in his decision to sell the team. I find it far more likely the team was losing money.