This entry is prompted by one misconception I've seen quite a bit of, but will likely meander into more general stuff, bear with me. Or you know, don't, nobody is gonna force you to read this.
To address that initial point, we start with Admirals, otherwise known as 'Flag' ranks. So called because they merit a personal flag (or they did back in the Age of Sail, I imagine in space navies such a tradition will have gone away unless you got some halyards on your star destroyer). How this worked exactly for, say, the Royal Navy in the 18th century I'm not really sure, but in the modern US Navy it's a dark blue flag with a number of stars on it depending on rank (so, a personal flag that's exactly the same as every other personal flag).
The term 'Flagship' is simply where the Admiral is currently flying his flag. 200 years ago this was important because it let you know which ship had overall command of a fleet, and who to follow in formation and so on. It also tended to change a lot depending on a variety of circumstances. So in other words, ships weren't designed as flagships, though Admirals of various stripes may have preferred certain ships (typically of the larger and more heavily gunned variety).
Now all this talk of signal flags and formation orders and the like is pretty pointless when we assume that even the smallest corvette has faster-than-light communications easily accessible. So why does this matter? Well besides the very specific distinction made via the Factory rules, there's nothing inherently special about a flagship. Granted, given a choice between a pocket frigate with a limited Command and Control suite and a 3000m Battlecruiser specifically designed to coordinate the actions of a large strike force, an Admiral is probably gonna go with the latter.
"Jesus Christ, Cyrus, the point of all this pedantry was...?"
Well for starters assuming your personal space navy is any size beyond 'six frigates and a tug' you've probably got more than one Admiral. This means you'll probably have more than one flagship. For a navy the size of, say, the One Sith or the Galactic Alliance, you probably have a LOT of Admirals, and therefore LOTS of flagships. In some cases, these are gonna be the massive two long beasts, but in other cases it'll simply be a little cruiser in charge of a pack of frigates. Main point being, the Alor, Darr Itah, Bar'sen Thor, and others (are there others? I can't remember...) are not attempts to skirt the flagship rules, and the info which says they are designed flagships refers to the part where they are designed for fleet command, not the somewhat arbitrary designation SWRP has about 5000m Dreadnoughts.
This could segue into a whole discussion about ship classes and the like but I'm sober right now so, eh, another time. (But seriously why are the largest general ships called 'destroyers' again?) Instead I'll touch lightly on officer ranks and what they could expect to command (in my heavily biased opinion, only loosely based on canon Imperial Navy organization).
Grand Admiral - In charge of a whole Navy. In the old Empire, in charge of the Navy an Oversector's Navy, or possibly just in charge of a single aspect of Naval Organization. Not terribly likely to be seen commanding a fleet, imo. The CNO of the USN does not ride out on a carrier and launch planes, he sits in the Pentagon and, idk, probably hates his life attending meeting after meeting after meeting. Most factions tend to assume that there's only one of these guys, which I think is pretty fair (the OS have two!).
Fleet Admiral / High Admiral - Assuming your navy is administratively divided similar to the US Navy (that is, different 'fleets' covering large geographical areas, these are the guys running those large purely organizational 'fleets.' Also unlikely to be seen commanding one on the battlefield, unless that whole fleet is out ready to rumble (see: Coruscant).
Admiral - You see how this is working right? This guy runs a subsector fleet, consisting of the combined forces from several systems. Alternatively, runs a high-profile system. In the OS Navy I had written that the Coruscant Defense Fleet was an Admiral's billet (specifically one Threnody Kun, courtesy of @Ajira Cardei. I imagine they were killed in action during the battle).
Vice Admiral - Runs your average system fleet. Once you get to here it becomes increasingly likely that the Admiral is going to take the field themselves. It makes sense, if your sector boss calls your forces in they'd be most used to working under their own Vice Admiral, and you need to break large forces up into manageable component groups, etc. etc.
Rear Admiral - Traditionally two ranks (upper half and lower half) because of ye olde royale navye traditione but that can safely be disregarded. Most any force large enough to merit a Star Destroyer probably has a Rear Admiral on said SD commanding the force. Worth noting that he is not typically involved in directly commanding the ship, that's the job of that ship's Captain. The Thrawn trilogy handles this pretty well with the way Pellaeon and Thrawn work together. Thrawn of course is a Grand Admiral, so you can already see that canon and I disagree on the details.
Commodore - A decrepit and archaic term which has a lot of confusing history (and which most people LOVE for some reason) but in most cases in the modern world is an informal/assumed title used to give a Captain authority over other Captains. Basically it's tied to a specific billet, and is not itself an actual rank, rather whatever Captain assigned to that billet assumes the title and authority, and reverts back to being simply a Captain once he leaves. Likely commands a small squadron, one that might not merit a Star Destroyer.
Captain - In my opinion the lowest rank that shoudl be seen commanding a Star Destroyer or larger vessel. Canon tends to disagree. Similarly, any larger vessel that has an Admiral on it will also have a Captain. The Admiral controls the fleet/force/squadron/flotilla/bunchofsquids the Captain commands the individual ship.
Commander - Heavy Cruisers, Cruisers, maybe small Star Destroyers, larger/more expensive frigates.
Lieutenant Commander - Smaller cruisers, frigates, corvettes, literally everything else worth commanding..
Lieutenant - Corvettes. Past this you start talking about really junior officers, who simply should not be trusted to be in command of a warship. There's exceptions, of course, maybe you put a bunch of experienced personnel on a patrol craft and just have a junior officer there to be the fall guy (er, boat officer) but generally speaking if you're talking a large Navy you've got no dearth of Lieutenants, you know?
There's also fighters/strike craft to consider, which gets real interesting in Star Wars because IRL that's officers again (with up to Commander still flying regularly) but it's made very clear in SW that you have enlisted ranks flying (a la WW2).
The above ain't gospel, and ain't meant to call anybody out. It's my opinion on the matter, formed because I got bored on the train earlier. Write what you want, though it probably couldn't hurt to do some research from time to time.