Circle of Flame‘s ability triggers when a creature without flying attacks either you or a planeswalker that you control. (It will trigger once for each of these attacking creatures.) When this ability resolves the appropriate attacking creature will receive one point of damage.
In most cases, flying creatures will fly over this circle and not receive any damage. However if for any reason a creature receives the flying ability after this ability has triggered it will be too late and it will receive damage. Circle of Flame’s ability does ‘care’ whether or not a creature has flying when it triggers, but it does not when it resolves. Unlike many other somewhat similar abilities, this ability does not contain the ‘conditional if’ clause. Because of this, once the ability triggers it will deal damage to an attacking creature even if it is flying when at that time.