I don't know about Amazons, but a lot of parrots chew on their feet when they are nervous /feeling anxiety...That's actually really common, and with some birds it's very much the same as "plucking" in that they intermittently chew on their feet every minute or so, like they're sitting there and they are constantly putting their foot in their beak and chewing on it (either their foot or their toenails)...And if it's really bad you can actually tell that the bird is doing it out of anxiety/nervousness, you can see that they are anxious by their eyes and the look on their face. No different than a person chewing their fingernails...
I'm sure they also do it because they have an itch, because they are using their toenails to do something that we can't really see, like pick at their beak, maybe their feet are dry, etc. It really depends on what is going on when they are doing it, and "how" they are doing it...I've seen it many times with birds at the Rescue, and you can absolutely tell when they are doing it out of anxiety...They will be sitting there on their cage-top or their stands, or on a shoulder, and they suddenly start lifting their foot to their beaks and start visibly chewing on either their foot or the toenail, and they'll keep constantly putting their foot down and then lifting it back up to chew on it, back and forth. And then if you look at what is going-on while the bird is doing it you can usually tell why they are anxious; maybe there is another bird out making them nervous, maybe they are in a new place and nervous about that, maybe they are on someone's shoulder and they are nervous about that, etc. There is usually something going on that is making them anxious and if you stop and look and think about what is going on, you can usually tell if they are doing it out of anxiety or nervousness...
If it's something that Amy is doing constantly no matter where she is or what is going on, then it's likely due to some kind of physical reason, like itchiness/dryness, or he's picking at his beak, etc. But if Amy is doing it intermittently at odd times, take a look at what is going on in the room/around Amy, and if he's doing it out of anxiety/nervousness you'll probably be able to tell...Also, if it's something that Amy started doing regularly since you've moved and wasn't doing it prior to the move like he is now, then that might be the answer...
Lita, my Quaker, does this out of nervousness occasionally. It's actually kind of sweet in a weird, demented way. She'll be sitting on my shoulder or playing on her stand, everything is fine and she's loving life, and then Kane (Senegal) will fly over, and there goes Lita, chewing her nails! And I actually say "Lita, don't chew your feet!" and she puts her foot right down, but inevitably if Kane is still around and comes near her, up goes the foot! She does it when Kane comes near her, she does it when she sees me carrying the toenail clippers (ironically), she does it when the carrier comes out and she knows she only ever goes in the carrier for a CAV trip, she does it when the Shar Pei comes near her (she's fine with the Cattle Dog, such a weirdo), etc. It's Lita's "tell" that she's nervous, and you can definitely see that she's nervous...It's almost like when she starts chewing on her foot/toenail it's like she's saying "Oh no, here comes the big green bird!" or "Oh no, she's going to clip my toenails!"...She's the only one of my birds that does this, but I've seen it many, many times with birds at the Rescue...It's very much like watching a bird start to over-preen/barber themselves suddenly when something makes them uncomfortable...I'd much rather Lita chew on her toenails when she's feeling nervous/anxious than she barber/pluck herself, so I'll take it...