Could Apple take legal action if Amazon were to try that? (hypothetically of course)
My understanding is not directly, however it could be argued that they were encouraging the end user to break the EULA on the product and thus interfering in the contract between apple and the end user. Different legal systems would view it differently.
On the other hand, apple could just throw more money into securing the phones from jailbreaking and end the business model much easier.
I don't think Amazon would want to launch a product dependent on JailBreaking. Unless Apple is forced to provide an API for alternative app stores, I can't see this ever being allowed. Unless of course apple rips off the idea and does it themselves.