Right after Kazi came to live here, because of his plucking issue the vet said he needed to molt and told me to up his fat intake for a while and encourage a molt. So I did (while feeding him tons of Vit A rich foods) and it worked. But he also put on a bit too much weight.
Flying is the best exercise, but it's not the only exercise. Kazi can't fly. He's damaged his primaries so badly they're not growing back in save the end two or three on each wing. So he climbs. He climbs everywhere, he climbs everything. If he wants to get to somewhere, I make him climb, I don't offer to help him get there.
But mostly we just cut out a lot of the fat from his diet after he molted. Kazi dropped some weight and is back down to a normal sized bird again.
Mal's seed diet is probably his issue. I bet once you get him on good food he'll drop a lot of that weight. We just recently got an amazon at the rescue, a red lored, who is just the fattest little bird I've ever seen. Amazons LOVE to eat and they love to eat even more when it's bad for them! Kazi seems to love anything orange, so sweet potatoes, butternut squash, carrots, etc. Dark, leafy greens are also a good source of vitamin A and calcium, but Kazi doesn't care for them completely raw, so I have to nuke them for a few seconds first. Of course, that holds true for almost all his fresh food. He's picky.
And yes, clipped birds, even freshly clipped birds, can fly if startled enough. And the feathers do grow back, so keep an eye on that. Lots of birds are lost because the owners thought they were still clipped and step outside with their bird on their shoulder. Actually, last few times I was at the Petco in Ranson (where Kazi goes in with me on my shoulder!) there was a flier up for a CAG that had gotten away from its owner. I keep my eyes peeled for that little guy all the time.