I'm probably wrong, but ever since Inquisition was announced and details were given, I haven't been able to shake off the impression that Hawke was originally intended to be the Inquisitor but backlash against 'em after DA2 made Bioware go "Nah, let's have it be a new character." He/she was called 'the most important person in Thedas' and unless Hawke set off some eldritch level Rube Goldberg machine of Flemeth that will result in the change coming to the world, I don't see that.
I don't remember who exactly stated it but I remember one of Bioware staff saying that an expansion had been canceled for DA2 so I guess that Cassandra wanted Hawke to help with the Mage/Templar conflict but not necessarily with the Veil Tear and/or The Inquisition.
From what I understand The Inquisitor is, if not The Founder, one of the new Inquisition first members. As for Flemeth, I dunno, I have a hard time picturing her as a real villain, I can agree that she has an agenda of her own and can be pragmatic at times but I'm not so sure that she should be considered as Thedas main antagonist. But I'm getting away from the initial subject so I'll leave it at that.
Also like Hinata Hyuuga I've been led to believe that the current Inquisition has nothing to do with the Inquisition that became The Seekers/Templars, even more so if we consider that the Inquisitor canbe a Dwarf, a Dalish elf (I don't actually know if we'll be able to play a city elf or not) or a Tal Vashoth. And I would expect none of those to be chantry followers.
The Inquisition feels more like a nickname that has been given to them and that in turn they adopted.