Powered armor and mecha would be few and far between, and used almost exclusively for urban combat(possibly even for COIN operations as well), where even hover AFVs will be hard pressed to maneuver.

Also, the Royal Guard should have forces more mobile than conventional infantry(something similar to the Irish Army's Ranger Wing), perhaps mounted on armed hover bikes or hover cars converted into Frontier-analogue FAVs/SRVs. 

@Jedi, modern combat doctrine stresses mobility and rapid deployment, especially given the fighting against irregulars.

I think a regiment or two of MBTs would suffice for the Royal Guard(possibly as Household Cavalry Regiments), normally detailled to patrolling the few open areas of water round the capital, as well as for brown-water operations in general(2300's hover tanks are capable of being used in blue- and brown-water ops as well as overland combat).

There would probably be a regiment of Household Cavalry mounted on robotic steeds, both for guard and ceremonial duties, and for defense of the cities themselves in case of attack. The robotic horse-mounted forces might even serve in the formation recon role in such unforgiving planets as Laco or Volturnus, as well as against Sathar scrubs and their attack beasties.

Also, some infantry units(dragoons)would be designated as Household Units as well, dedicated to royal protection. 

Spec forces wouldn't use powered armor, as their credo would be to travel light and strike fast.

Definitely plenty of Meteor assault shuttles, but that might bring up the issue of just whose assets they are(like the A-10 debate between the Army and the Air Force).

Plenty of room for robotic arty platforms in the hover artillery(with the artillerists sitting in an Explorer or similarly highly-mobile vehicle passing on the bots' firing orders).

I would think that hover artillery would be able to fire on the move.

In addition to hover artillery, we would probably have a corps of the Royal Guard dedicated to manning the ortillery and planetary defense batteries, and another manning fighter craft(which can be used for close orbital defense and air support, freeing the Royal Marines up to man the bigger ships).

Also, you would have hover arty units dedicated to air-defense duties as well, able to zip around from point to point to supplement the fixed planetary defense emplacements.

In retrospect, I wouldn't see much use for mecha(except for the robo-horses) and powered armor in the Royal Guards orbat; these would mainly be Landfleet assets, since they lend themselves more easily to rapid deployments and planetary assaults than the hover AFVs seen in the Dragon magazines.

On the other hand, you'd definitely see a great deal of aircars and jetcopters as hogs, slicks, and dustoffs, with larger aircars and jetcopters performing as hogs and slicks simoultaneously. These airmobile formations would work closely with the mud hens assigned to the hover infantry(with these infantry possibly even equipped with jet packs to enhance their mobility)in highly-mobile formations capable of tackling any role from conventional combat to COIN operations.

(BTW, for those unfamiliar with Vietnam-era terminology, hogs=gunships, slicks=troop carriers, dustoffs=medical evacuation).

I would say air cav would refer to the hover infantry as mud hens or something similar. The Royal Guard would probably officially refer to the hover infantry as "dragoons," as at least one brigade combat team of Stryker-equipped U.S. Army soldiers are now(the 2d U.S. Dragoons), to reflect their high rate of mobility.

One more thing: The Guards might also maintain specialist units for, say Alpine ops on the planet's south pole. They would be small in number and relatively light on firepower, but effective in their chosen field of endeavour.

Also, thanks for reminding me of what I forgot, air and naval gunfire support capabilities. The Royal Guard would probably have a couple of Air/Naval Gunfire Liaison Companies(ANGLICOs), if not a Naval Gunfire Liaison Operations(noglo)specialist attached at squad level.

Alternatively, an individual Guardsman's weapon's own targeting systems could be networked to fire-control computers on air, orbital, and space assets, allowing him to paint a target to be taken out by airstrikes, orbiting starships, or orbital weapons platforms.  

It wouldn't be the only standard-issue infantry rifle, of course. Guardsmen would also be issued with rafflur weapons(specifically made to Royal Guard standards) such as the Mk 22 Particle Accelerator New Technology Rifle(PANTR, pronounced panther), equipped with a built-in targeting laser and all the other goodies the LION would have.

Also, for long-range sniping, and situations where lasers might not cut it(e.g. if the bad guys have albedo screens), Guardsmen would also be issued the Mk 21 Technology Improved Gyrojet Rifle(TIGR, or tiger), which would use needler technology to accelerate the rocket, so it would be useful at point-blank range, as well as beyond point-blank range. The WarTech TIGR would also have a targeting laser, grenade launcher, and the optics of the other two rifles.

All the rifles would, of course, come with bayonet lugs, as a just in case, with a choice between vibroblades, and, maybe a proton bayonet based on Shadow's Rafflur M-0.

Now, on the subject of flamethrowers: They're good for cleaning out troops dug into defensive works—caves, pillboxes, tunnels, and the like—as the Army and Marines demonstrated during the Pacifici island-hopping campaign during WWII.

They're also of some use in COIN operations(flushing or burning out ambushers from their cover).

That said, flamethrower troops will be few and far between, and, almost always robots, like you said, Jedi, since no sane commander would risk a lucky shot to the tanks turning one of his organic troops into a flaming charcoal briquette when there's  robots to do that kind of suicidal grunt work.

These being highly-specialized units, flamethrower bots would generally be assigned at battalion level and up, unless the troops are up against enemies holed up in caves or other defensive works on a regular basis(or engaged in operations against Zuraqquor hives on a regular basis).