Is there any way to play a FFA with the friends in your party? If no, is there any reason for this? I can't seem to figure out the settings to set this up.
Just go to multiplayer, create game, and select the map you want to play on. On the right side, set the mode (where it normally says 1v1, 2v2, etc) to FFA.
As for the quick match FFA, that is not possible to do with a party, probably to prevent a party playing them as a 3v1 or abuses of that sort.