I think... The Killer Swarm takes this, depends.
Kumongo would immediately begin shooting web at the trio. Anguirus may dig underground to sneak attack it. That is where Megalon comes in, burrowing underground to meet it head on. Rodan may fly out of the way, and pit itself against Megalguirus. Megaguirus is not big on defense, but she's got insane speed.
The only way to hit her is to predict where she'll be, or catch her attacks head on. I can see her spin circles around Rodan and impale him from behind with her stinger, sapping him of his energy. And if she grabs his wings with her claws, he'll be unable to do anything because he doesn't have an offense if someone grabs him from behind.
Godzilla... if he tries to head off and tackle Kumongo, the giant spider would simply jump out of the way and continue to shoot webbing.
Anguirus would be too busy fighting Megalon(they may be at a stale-mate underground), Rodan would be rapidly weakening from Megaguirus. And Godzilla would start to find it a lot harder to move around with all that thick coating of web on it. Eventually Godzilla's immoble, Rodan's too exhausted to move, so it'd only be Anguirus against all three.
If he somehow defeats Megalon, then he may put up a good fight, staying underground, attacking Kumongo from below, or drag the spider underground to kill it. Megaguirus wouldn't be able to do much even if she caught him, because she'd only meet with a back full of sharp spikes.
Then, after Anguirus defeats Megalon, he would do fine against Megaguirus. But only if he manages to catch her while she's off-guard.
That's if they fight one-on-one against each other. The only way I can Godzilla and the others win is if they work as a team. It'd be difficult, but not impossible.