Both Burst coin and Storj coin have announced they intend to develop decentralized storage facilities, but I don't know if either of them have actually done it yet.
As far as I know, Burst is PoC, which is interesting in itself but won't allow for decentralized storage. If I missed some info about Burst, could you link me to where you read about this? I am interested.
Storj on the other hand is a blockchain-based decentralized cloud storage platform. We currently have a working early version of our file-sharing application MetaDisk available at
http://node1.metadisk.org/ and we
expect our DriveShare application, which will allow users to rent out their excess hard drive space to the network, to be out by the end of this year. Take a peek at
https://github.com/storj if you would like to see how far we are!
Some links for more info:
http://storj.io/http://metadisk.org/http://driveshare.org/https://twitter.com/storjproject