As far as I know, nobody ever suggested that the Czechoslovak flag be changed after the Communist took power. There are probably two reasons for this: most obviously, there's nothing ideologically troublesome on it. No religious symbols, nothing associated with monarchy, just three colors in a cool pattern. And since this is the flag that everyone flew when celebrating liberation in 1945, and which represented the statehood and sovereignty that had just recently been renewed, it's likely that the Communists felt some attachment to it, and so did pretty much everyone else. The more complex answer is that there was no particular moment when the Czechoslovak Communists stood up and said that there had been a revolution and now everyone was going to live in a Communist regime. The Communists did essentially take control of the government in 1948 and implement a one-party dictatorship, but that's not how they described what they were doing. Rather, they said that they were renewing the postwar National Front coalition government and purifying it of reactionary influences so that it could better represent the will of the Czech and Slovak peoples.

The Czechoslovak Communist Party in the years after World War II was extremely nationalistic. They described themselves as representing the nation's best traditions, and their policies as basically the culmination of the Czechs' and Slovaks' historical destiny. Their strategy was to co-opt national symbols for their own political purposes, not to create new ones. This makes the Czechoslovak Communists very different from the Polish or Hungarian Communists, who had a much more complicated relationship with their national history. (For what it's worth, though, the Polish flag wasn't changed either.)

Also, Czechoslovakia's official name remained the Czechoslovak Republic until 1960, when a new constitution was adopted and it became the Czechoslovak Socialist Republic. They adopted a new coat of arms at this time as well, which totally remade the Slovak coat of arms in the middle of the Bohemian lion and put a socialist star over the lion's head. I don't know why this decision was made, to be perfectly honest. I could speculate, but I don't know enough about this period for my speculations to be worth that much.