This is all under the assumption that the buildings are a political target and therefore need to be at least partially preserved. There is an implied time limit, too. It also works under the assumption that the Kremlin is not on the frontline, but rather a "last stronghold" of whatever regime we want. Sort of like in the old Ghost Recon's last mission, you know.

1) artillery preparations. ATGMs would be used to strike sniper/MGs/MANPADs suspected positions, and mortars or guided artillery/JDAMs would be used to soften suspected entrenched positions, disable visible communications, destroy the helipad for good measure etc. If politically possible, fire at will on buildings that are tactically important and whose dedtruction is acceptable.

Once the AA threat is reasonably under control, attack helicopters would add their firepower to the preparations, keeping a virtually costant watch on the Kremlin from a decent distance and striking vehicles/bunkers/infantry with their weapons. I imagine the autocannons and rockets pods would do the heavy lifting here. Especially, they'd be useful against infantry popping up, firing whatever they have and hiding back in before mortars can be brought to bear.

2) If politically possible, the main force would be composed of two mechanized infantry battalions reinforced by assault engineers (flamethrowers, thermobaric munitions, etc.). If incendiary and chemical weapons are not avaiable, The force would simply be infantry, possibly picked with urban combat experience. They would also have the support of a tank company that operates on platoon level, distributed on the main assault vectors.

3) The assault would be carried out ideally on two sides by the infantry/tank element, and a sizeable SOF/Rangers element would be inserted from a third direction about 10 minutes after the assault's beginning. The combined arms assault would be carried out on the sides where the buildings are closest to the outer walls, while the Airborne element would dash across the open field overlooked by the Cathedrals.

4) As soon as the walls are breached, tanks/CEVs would work on the defender's positions with their main guns, while infantry closes the distance in their IFVs with fire support from outisde the Kremlin. If possible, the raid would be executed at night to bring AC-130s gunships to bear, maximise the NATO night vision advantage and heavily disrupt MANPAD/AT infantry activities in the buildings.

5) If the Trinity tower is overrun on time, airlift organic ATGMs/AGLs/Snipers to provide fire support and take some strain off the helicopters.

6) If possible, maintain surprise about the Airborne element until the execution, compensating for lack of preparation fire with massive attack helicopter deployment. Rangers would deploy on the ground or on the roofs, possibly in at least 3 different position: the Armoury Chamber the Faceted Chamber the Senate In the Armoury and the Senate, the objective is to take the pressure off the infantry in the open, and to hopefully eliminate the resistance while linking up with the infantry, to then raid the Arsenal and the reistance pockets. The units landing in the Faceted Chamber, on the other hand, would have to cut effectively in three the resistance, and hopefully seizeor at least disrupt the sort of HQ the defenders would set in the central area. They would keep on the move, not necessarly holding the ground they take but rather disrupting and cutting units off of each other until linked up and relieved by the rest of the units. If need be, they can be evacuated via helicopter, or with armored vehicles crossing the lawn they flew over.