This will be tough given their business model. Plenty of very strong android phones can be bought for free on contract, and off contract phones have already scratched <$100 for okay android hardware.
Amazon said their strategy with the Fire was to make it as affordable as possible. They know they make their money back in app/book/video sales. However, there is no room for a budget Android phone any more. The only way they can conceivably go is up towards the high-end, but that seems antithetical.
Only real selling point I can see for an Amazon device is video from Prime, which would require good data plans that I doubt major carriers would be happy to offer.
Perhaps we'll see an Amazon Wireless soon?