I think Flemeth transfered her soul to a younger and WILLING body, possibly gaining power of the Dread Wolf (what's left of it anyway).
Wasn't it said (by Morrigan, if memory serves me right) that Flemeth can only transfer herself to someone related to her (daughter, grandchild, etc?). Of course, if she'd read that in the grimoire it could be wrong. And then of course there is the whole thing with Flemeth saying she can't transfer herself into a host w/o them being willing. Could be lying, could be the stipulation of /her/ magic. From what I figure, neither of them were happy, things did not go as they needed to be (clearly), so I'm more convinced that they either fused together (Flemeth said Mythal was a part of her - akin to a human and their heart - and no doubt this is similar to the whole Anders/Justice thing, if clearly on a larger/more powerful scale) more than anything. Perhaps, with a strong will - as Flemeth mostly proved (we don't know what she was like pre-Mythal absorption) - one can keep their personality mostly intact (Anders tried to but he was pretty fractured by the end) so maybe Fen'Harel/Solas is going to be the more dominant personality.
Of course, with that expression Solas has when he looks up (yay glowing eyes, glowing eyes never seem to be a good sign in these games), it is entirely possible that he played her. But I'm not honestly leading towards that, moreso that he once again had his full power and who doesn't like the feel of godhood? If only because Solas was unapologetically who he was (other than the whole secret god identity thing), that is - an Elf and a good person. Good people make terrible decisions and good people can do awful things because they genuinely think that it is the best option (see: the orb). I also doubt Flemeth would let herself get involved in anything that wasn't part of something that would serve her revealed goal (avenging Mythal). So there's always the possibility that she'll end up the dominant personality if that chance remains. I'm not leaning towards a particular, honestly, I'd love a good pure fusion and see that kind of being comes out of that.
And then there's the whole thing of soul transference vs absorption of souls. Might act a bit differently if he absorbed rather than took in, if that meaning makes sense? Converting everything, somehow, to pure power instead, but I'm not sure if that's even possible. Don't even know if there's actually a difference in this world.
Speaking of the gods, a small non-sequitor about how I've seen people going "well they aren't gods they're spirits" re: the pantheon. What makes a god a god? Power? They might need some, but what, imo, makes a god as such is worship. Whether spirits or super powerful mages, what is clear is that they were worshipped by the People, which in turn bestows a power of it's own, socially for sure, and in this case likely magically as they probably were also able to attain power through the rites and rituals dedicated to them through their shrines, etc. This is more speculation on my part, of course, but even if they're not the big creator god/The Maker (which didn't someone say the writers were always going to leave that vague? I hope so, not really an approachable deity imo) that doesn't mean they're not gods in their own right. Reminds me of when Sera was saying how the Maker and the elven pantheon can't exists, why not? Because it doesn't fit one's monotheistic beliefs? The elven gods might not have created the world but they certainly played a clear role in ancient times.
I doubt that tangent makes sense but I needed to get it out of my system.
At this point I'm just hoping for a full expansion or another game to get more insight on this (we learned more about Flemeth in a few short cutscenes in this game than all the other times in the past two games, I really don't think she's done yet).