Can decentralized blockchain technology like bitcoin be used to store medical information? For example patients get private key, providers get public key?
The blockchain is used for more than just storage of data. To store data, all you need is a harddrive of some sort. What kind of things would you like to be able to do with this 'medical blockchain'? 

I think that in general, everything medical would be considered confidential, so even if it could be stored in a blockchain, no one would want to.