First of all, you might want to expand this concept. It doesn't bring anything new to what anyone thinks of when brainstorming on 'Faction Flagships'. A one of a king big ship with big guns that does big explosions.
'huge maintenance costs to fly them' - Exactly how huge, what kind of costs. Fuel, maybe? Expendable ammunition? All this has been already thought of and presented in earlier drafts of this concept.
'the immense amount of effort means only factions/groups of factions can feasibly operate one' - Since the obvious limitations of the game limit any ship able to be flown by one player at a time, I have no idea what you're thinking of about 'operating one'. Huge costs in building one in POS' is closest I can think of. And this has already been brainstormed on as well. They're pretty logic things, obviously.
Trading factions having flagships doesn't lead me thinking of anything else but Custom Barges. Regardless of how one would balance such a ship, it would end up either too overpowered(regarding powertrading), not any bit more useful then a current Barge, or simply too demanding in comparison to the advantages it would bring, that would render it useless.
Usage in military factions brings the most obvious benefits, but with obvious drawbacks. First of all, balance drawbacks. The amount of agility you'd give to such a ship in order to keep it 'realistic'(the freelancer kind of realistic) would make it either: a) a big Valor on steroids, b) a big Green Brick of Doom on steroids, c) a big Lost Battlestar on steroids that takes 10 minutes to turn around. I'm saying there's no way to keep such a ship balanced, in a way that would make flying it enjoyable.
So the only reason someone would want one would be the visual appeal of such a ship, or the roleplay one. And that can already be accomplished by simply increasing the reputation of a ship ingame. Take the Hellfire Ven'Gyr. The sheer reputation of the ship allowed us to use it on at least one accountable occasion by simply roleplaying in local comms the arrival of the ship in the next few minutes. At least two dreadnoughts retreated. And this all happened in the past few months, while the Ven'Gyr was, and still is, nerfed.
Link flagships to player bases, and add the probability for equipment being lost if the ship is destroyed. If equipment for said ship is produced via player base supplies. And if the ship is not destroyed, but simply damaged, the repair costs would be high.
You'd imagine that to make a faction flagship, in theory you'd need the following things...
A maxed out POS.
then you manufacture the various 'components' of the flagship, with their own costs. (actual amounts can be decided)
I have no idea what Trading factions would want. Barges would be probably the thing, as you've said.
You're assuming that faction flagships need to be big. They need not be. Hypothetically, the LN flagship could just simply be a Liberty Dreadnought with similar handling, but souped up powercore and hard hitting turrets.
These ships are not to be balanced in the traditional sense of the word. Considering the costs you need to make and fly one, You'd imagine they can really dish out damage against opposing capital ships. LN flagship could maybe take on 3 turtles and win. Or so.