I don't think it's been spelled out in DCA/3E, but in 2E, it was stated that matching any descriptor is as good as matching all descriptors. So, if you have a magic flaming sword with Slashing, Fire, Magic, and Physical as descriptors, it will be useless against someone with Immunity to Physical damage because the descriptor matches the Immunity. When used against someone with a Vulnerability (Magic) Complication, it does the extra damage because a descriptor matches. If there's a combination of both, use your best judgment (i.e. someone with Immunity to Physical Damage but Vulnerability to Magic might not be hurt at all, but someone with Immunity to Physical Damage with a Power Loss against Magic would).
If you want a slightly more complex take, the rules more or less state that effects can stack, so you could build your magic sword with damage 7 as being 3 damage from the flaming aura (Magic, Fire descriptors), 2 damage from the sword's edge (Slashing, Physical), and the +2 damage from your strength (Physical). Against someone with Immunity to Physical Damage, you're still doing 3 damage from the flaming aura. Against someone with a vulnerability to fire damage that means they take half again as much damage, you might only add one to your damage (3/2 rounded down to 1). It definitely makes things more complicated, but it prevents a bit of player frustration. And, of course, you can always ad hoc the breakdown although my experience is that players tend to prefer consistency and knowing what will happen in a given situation.