Clone a device to recover my mined BTC

Is this app in some way tied to the serial number of the device? Just wondering why you are talking about "cloning". Do they not provide some way of migrating your app and account to another device?

Anyway, there is no way of taking an image of the device which will include device identifiers (and in some countries it would be illegal to modify such identifiers). More importantly, if you could take an image of the device (and a nandroid backup is the closest thing to this) it would only work on another device of the same model, which would not solve your problem. If you tried to put it on a different model the best case is that it wouldn't boot afterwards - the worst case is that you might corrupt the bootloader and so permanently brick the device.

Yes, you can get cyanogenmod for many models of device, but it has to be built for each model individually. That's the way mobile operating systems are.