Doesn't look like you can. Other icons can be moved or swapped after a long hold (dotted ring around the icon) while in the apps screen but the Alexa icon seems locked in (long hold not possible).

 

That would have been the perfect solution. Just implement it like they do every other app and let it be moved as the customer wants. I'm thinking there must have been an Amazon "product placement" revenue involved. No way would they hijack the entire UX pattern based on "customer demand". I think that on the fact that I don't recall a single post along the lines of "I wish I had Alexa" pre-3.0 chatter.