Unfortunately the previous poster is correct, I am not aware of a way to do this cloud to cloud - if someone does, please speak up.
However, if you're willing to do a little setup in your house, you can have a pretty seamless experience.
I buy almost all of my music from Amazon, because they have the best deals, larger library, and they auto upgrade the audio resolution for you when they get better copies of their files.
I, however, play almost all of my music via Google Play Music. The interface is superb, as are the organizational principals, and playlist curation.
So, my solution is pretty simple. I have a server in my home running Windows 7 for various reasons. I have Amazon music manager running and set to download all new purchases to a specific directory. I have Google's music manager running all the time as well and looking at that same directory for new deposits. When it sees a new music folder if uploads it to Google play music.
The end result is that I can be on phone anywhere in the world, buy music on the Amazon app (or, more magically,. Hit the buy from Amazon button in Shazam), and the purchase goes thru, downloads it to my house the reloads it to the Google cloud. The music appears in my Google play library within a few minutes. Poof.
Therw is an additional advantages, in that I now have three copies of all of music: Amazon, Google, and my home server. Overly redundant, yes, but... Uh... I'm quite anal that way.