No.
Barugon's weapons both utterly failed to kill Gamera instantly, and Anguirus is arguably the closest thing in spirit and protection to Gamera in the Toho kaiju pantheon. I do not think I'm the only one to remark on that similarity, but even if I am it's not a wild comparison.
One might say that Gamera likes heat, and that is why he was not harmed by Barugon's rainbow. However, the rainbow's effect was more akin to disintergration than sheer heating; this evidenced by the wreckage which remained after a rainbow attack, and also by the survival of mirrored glass in the midst of the effect. There was also the arcing of the rainbow to consider, as well as its seemingly unimpaired functionality from underwater. The rainbow was some kind of steerable field effect, not a simple heat ray.
Gamera's frolicking in the rainbow didn't result in any visible damage at all. Given that his shell left large areas unprotected, I conclude that the rainbow was not an optimal anti-monster weapon. (This also explains why Barugon was not killed when the military bounced his rainbow straight into him. Hurt badly, yes, but not killed even by a direct hit.)
In contrast to the rainbow, Barugon's freezing spray took Gamera out of the fight - but still not instantly. Gamera still managed to put a claw in Barugon's head before freezing completely, and Gamera is the giant turtle which craves heat. Also note that the frozen, heat-loving turtle managed to unthaw after a while; he was out of the fight, but by no means dead. Incapacitation, but not instant.
Now, Anguirus has a bit of a following because of his spirit and ruggedness. He also didn't seem to mind a cold environment, though that doesn't imply that he couldn't be frozen by some chemical mist. I do see Ang as being less vulnerable to the mist than Gamera, who still managed to survive it. That means Ang should get a few extra seconds to decide to attack, run away, [i]etc[/].
As for the rainbow; I've no doubt it would hurt Anguirus. He doesn't react well to being zapped... but while he doesn't like beams and explosions he still survives them. Gamera easily survived the rainbow even though it wasn't a purely-heat weapon. Anguirus, who has a fair amount of armor on his head and back at least, seems likely to survive the rainbow, at least long enough to scurry away.
Barugon should win a fight against Anguirus, but one-hit kills seem rather unlikely to me. He'd have to put in a little bit of effort.
As far as the KG/Jiger match goes, Jiger essentially bought it from a big stick to the head. 'Credit to Gamera for having a good throw, but that's not exactly super Jiger durability. One Death from Above by KG ought to crush Jiger pretty convincingly.
Jiger's one main weapon - the "skeleton ray" - fires in an arc just like Barugon's rainbow, and doesn't appear to be well-designed for anti-flier use. Jiger could conceivably take to the air trying to get a good angle for the ray or even "solid saliva spears," but King Ghidorah's a far better flier and does have those gravity bolts.