A player has to choose on Grand Company (later they added the ability to change, progress is independent of each grand company you join).
Free companies are associated with a Grand Company.
Free companies are comprised of members from all three Grand Companies.
Frontlines currently allows you to only represent your Grand Company.

Frontlines should allow you to choose your Grand Company affiliation or your Free Company's Grand Company affiliation in the Duty Finder window. As a player who is an Immortal Flames that belongs to a Free Company that is based off of the Adders. I don't see why I can't help either side, I'm already doing so through my free company.

There, lore and player options.