I am thinking of ideas to use the new Satyr Firedancer from BNG, and I was wondering, How would a card like Flames of the Firebrand work with him? Could I say I deal one damage to my opponent three times, thus giving me the chance to have the satyr deal one damage each time to different creatures, or would all of the damage be dealt simultaneously, and I can only deal three damage to one creature?
If a spell requires multiple targets but the types of those targets don't overlap (like player) then you can only target that object once. Then for Flames of the Firebrand you choose the values assigned to each target so that every value is at least 1 and the values must add up to 3. Then when the spell resolves all damage is dealt simultaneously and so your opponent takes damage only once and so Satyr Firedancer triggers only once. Now if you're in a multiplayer game then every opponent you choose for Flames makes Satyr trigger so if you deal damage to two opponents then Satyr triggers twice.
Now what I mean with types overlapping is that if for example spell says 'Destroy target creature and target land' and your opponent happens to have an active manland then you can target the manland with both targets.
So a card like Aurelia's Fury would also just target the opponent once, even if X is, say, 4?
You are correct, if you are dealing all of X to a single target then it isn't being divided. Mana Clash would allow you to choose a target creature for each separate point of damage though.