While none of the floo flames are missable, there are a few that are locked behind some of the main story quests. The Map Chamber and The Room of Requirement are two secret rooms that will be unlocked during the main missions "Jackdaw's Rest" and "The Room of Requirement." All other floo flames can basically be found any time after you've gotten to the point of the game where you can free roam in the world.
It is recommended to wait until after you have the broom unlocked to go after this though as that greatly speeds it up.
In order to activate a floo flame you simply just have to walk up to it, and it'll activate. Honestly just get somewhat nearby and it'll activate as the range on them is pretty far for the open world ones.
(Main Quest #18: Jackdaw's Rest)
(Main Quest #21: The Room of Requirement)
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