Siradix wrote...
I'm assuming that the dominate soul of the two is the one who gets to keep the body then. Which could explain the Robe of Possession.
I do not, and cannot, know how Bioware and its writing team will or would handle this.

That said, in general, the most powerful of the two would end up with the body (if it's a situation of two souls being unable to co-inhabit it). Nevertheless, this isn't always true, because of other factors. The two factors that most commonly lead to a less powerful entity in possession of the body are:
* the less powerful entity takes the more powerful one by surprise - as in physical combat, the person who springs a trap or surprises an unsuspecting victim has an advantage
* the more powerful entity is young and inexperienced - in this case, they may be unaware that such a thing is possible, or simply unaware that they are at risk
It should also be noted for the purposes of this discussion that Flemeth also has the advantage of a blood relationship - frequently stealing the body of another is made much easier in the presence of a bond between the two. Blood is one such bond. Sex is another, of course, and victims are sometimes surprised and 'taken' during such an act. Other methods exist - rituals, objects of power (like the robes, actually, so Flemeth really is covering several bases), training of the victim (Flemeth covered that one too) so that their body and mind are 'prepared', to name the ones I can think of offhand.
If it's a demon in charge of 'Flemeth', then that demon may not have the blood link. That's not something I've encountered before, lol. Because although the two bodies would be linked, the demon and Morrigan would not be. Although, I suppose, the preparation and training could have done that.
To be honest, my gut feeling is that neither Morrigan nor Flemeth lied to us - concealed things, yes, but not lied. There is sufficient wriggle-room in what we've been told that it's easily possible to envisage multiple options. Why bother lying (and potentially being caught at it) if you can avoid, evade, and be mysterious?
There is insufficient data on which to found any hypothesis. All of what we're discussing is simply unfounded musings. It's fun, though.