How does Amazon make money no this?

A few things.

One, the early price for the fire phone was insanely high. It was not a good enough phone to command "flagship phone" prices, but everybody and his brother would like to make "flagship phone" profits so they gave it a shot.

AMZN seems to be the one company that Wall Street doesn't pressure into making a quick buck. They don't feel a lot of pressure to make their overall operations profitable because investors are still buying the idea they can spend money to grow.

Also AMZN can make the claim that the Fire Phone is going to pay off through "synergies"; if these people become prime members, buy a lot of Kindle books, get a Dash Button, consume AWS, etc.

I don't think they are trying to make money on this anymore. I believe they have hundreds, or maybe thousands, of these phones in their warehouses that they have been unable to sell. At this point, I'm guessing they are just trying to recover as much of their investment as they can.

Well, they have the android appstore: http://www.amazon.com/mobile-apps/b?node=2350149011