Before I get started, I just want to point out that I'm looking at this from an "accuracy" viewpoint, to help suspension of disbelief (I appreciate that there are plenty of...inaccuracies in the game, but most are either required for game play reasons or do not harm suspension of disbelief) rather than a traditional "MMORPG" or general online game view of rankings as such. There are a few gameplay modification ideas in here - these are more me thinking out loud as to what I would consider a way to make it more accurate in this regard, and I fully understand if such are impossible for one reason or another. I would add that I have taken a good look into canon ranks to try and expand this as much as possible.
To whit, as it currently stands, the ranking system is perfectly sensible and in line with a reasonable idea of military heirachy until you hit Rear Admiral. Lieutenant's command small ships, Captain's very big ships, etc. However, Admiral's commanding only a single ship seems a tad iffy and out of place both in Star Trek Canon and Star Trek Canon - really they should have more then one ship under there command, but I shall get onto how I think this could be implemented at the moment. So that no changes to the actual gameplay need to be made at the moment, the best first step I would suggest to remedy this would be to restructure the rank system so that the ranks, as they currently stand, are alll below flag rank.
This would be simple enough - either have the tutorial as a cadet, then start as an lieutenant junior grade, lieutenant, lieutenant-commander, commander, captain. This is the same number of ranks as now (I appreciate that Rear-Admiral is currently split, but I think that this is rather unneccessary and in fact I can find no cannon sources for USN style one and two star ranks. In fact, all the ranks seem to be USN ranks rather then Starfleet ranks). Thus, someone who is now a Rear Admiral would be a Commander, etc.
After this, you can introduce the rank Fleet Captain, then subsequently the flag ranks of Commodore (why has Commodore been ignored? Perfectly cromulent rank in Starfleet), Rear Admiral, Vice Admiral, Admiral. I would avoid Fleet Admiral, as that would be the professional head of Starfleet, and would just concern shuffling paper and the 25th cenutry equivalent of sticking pins on maps - not exactly in the vein of the game! Plus, the nature of MMORPG's means there always needs to be someone to give you orders.
Now, the obvious concern I'm sure some of you have is that this would mean that you would be demoted. I have a solution to this, though it's not something I've found existing in canon sources, but it is a historical military practice and would make some sense in the setting. Simply put, you're old rank becomes you're Brevet rank. I won't go into all the details that this used to entail in the British Army, but simply put (and for the purposes of STO) this is an honorary rank. Someone who is now, say, "Vice Admiral Jerry Squigglepops" would become "Captain and Brevet Vice Admiral Jerry Squigglepops". Not a perfect or elegant solution, but a solution none-the-less. It's pronounced Brevvee, BTW

Now, this leads onto the question of what to do with Flag Officers. Well, the solution would be the give them fleets, with various sizes of fleet and types of ships in the fleet depending on rank. For example.
Commodore - Small Flottilla - 2x tier 1 ships
Rear Admiral - Large Flotilla - 3 x tier 2 ships
Vice Admiral - Small Squadron - 4 x tier 4 ships
Admiral - Large Squadron - 5 x tier 5 ships.
Again, just an idea - others may have better ways of dividing it, etc. II have not used the term "Fleet" for the reason of ambiguity.
Obviously, I don't think there should be too much detail regarding the other ships in your flotilla or squadron - perhaps they could come in "Engineering, Tactical, Science and balanaced" packs, you could have the ability to appoint captains, and "general equipment packs" - of the "common, common, rare, very rare" mould., but it wouldn't be neccessary to appoint bridge officers and consoles and weapons, etc. to all these - just an overarching "kit" so to speak. For PvP (and the current PvE) play, I'd only have the flagship involved. Keep the fleets for story-type missions.
And while we're at it...where are the bally enlisted personnel?
Again, please just take this as mere musings...more me thinking out loud as to what I think would be nice, not shouted demands to "OMG change this or communism will take a hold" or what have you. I'm a bit of a military heirachyology buff, and military history wonk, hence I freely admit my perspective is very skewed about all this. If you want someone to waffle about the perculiarities of the Rank of Commodore, the evolution of Brigadier in the British Army, why Silver outranks gold in the US forces, etc. I am available for weddings, bah mitvahs and wedding anniversaries :P