I have the same problem as you and have just found a way to do it.
- Download ifunbox, its FREE software that views your iphone/ipod/ipodtouch etc. as though it was a hard drive so you can explore the directory of the device
- Download any songs that you want from the cloud player service to your device
- run ifunbox and go to the following (or similar) destination on the device "User device/User Applications/Cloud Player/Documents/CloudplayerDownloads"
- Select the tracks that you want (they probably wont have readable titles but thats ok because when it copies them to the pc it should recognise the track names) and copy them to your pc by clicking "copy to pc"
- Select where you want the files to go and save them.
- Using itunes copy to the appropriate device. (you might have to convert the files to the right format, i havent got that far yet i wanted to tell you before i forgot, but i dont think so because they are mp3 when you download from amazon.
I have just done this with the new Black Sabbath album which i bought in vinyl, where are i am staying for the next few days has limited internet data but my phone has unlimited data so im going to use that instead
Hope this helps