The short answer is no.

First, for several reasons a lot of data will not migrate to the cloud. The Cloud certainly has a place, and I make extensive use of certain services, but there are some things that for a variety simply will not fit there for the forseeable future. For one thing, if the database is anything truly mission critical than many executives are leery of loosing control over it. For another, use of the cloud does bring up privacy and security issues that can be challenging to work out if the data is at all sensitive. And finally, there is the loss of, at least in some cases, the ability to fully customize the service.

Even with data that does fully migrate to the cloud, in most organizations the DBA is the person most knowledgeable in terms of properly structuring it and protecting the logical integrity of the data. So, in that situation the DBA may shift more towards a Development DBA/Data Arhitect but there will still be plenty of room for the DBA.