Amazon has obviously forked Android successfully and has sold a lot of tablets. OPhone is an Android derived OS used in China, and other Chinese OEMs without access to the Google ecosystem have to do similar things.
Microsoft has a different set of problems. Windows Phone is already shipping, so adopting Android would actually delay the next release. What they need is a stronger ecosystem—more apps to bring users and more users to bring developers. Adopting Android might help them achieve that, but at the cost of ceding control to Google. At the end of the day, why would anyone buy Android from Microsoft instead of Google?
If they can't make a success of Windows Phone, MS would be better off to just can it and provide apps and services to both iOS and Android.
The kindle isn't successful because Amazon was able to eject compatibility concerns, it's successful because Amazon was (unlike basically all the other variant Android customizations) able to bring elements to the platform that customers actually wanted, and that these outweighed their desire for interoperability with the Google GMS ecosystem.
Windows CE was un-competitive with Linux, so they had to go to an NT-derived kernel and "real Windows" userland elements for the core OS. But those are bloaty and suck batteries and need fast CPUs.
I don't think they should exactly adopt Android, but they should, at least, have considered doing something Android-like. Imagine the .NET runtime on Linux. That would be very Android-like, but compatible with .NET languages and the VS toolchain.
That was true until the moment they spent $7.2 billion acquiring a company and 30,000 employees that need to make (and sell) devices to keep going.
MSFT now has an interest in shipping hardware that will compete with their software interests.
What amazon has successfully done is build a kindle based on linux as opposed to whatever is on the original kindles. It's a very limited thing and nothing more than a kiosk to amazon purchases.
The only reason people buy it is because of brand loyalty to the kindle device series they knew before.
The root process for Kindle devices is very annoying. However, there is a reason why most app store apps don't work on Kindle. Unless a developer is specifically thinking about supporting a device without Google APIs, they are likely not to correctly handle when API calls fail or aren't available. Also, the Kindle Fires to date have had some quirks here and there that don't work exactly as you would expect, so a developer would probably have to actually test their app for Kindle (which is its own pain due to how bad the Amazon developer portal is).