What are the licensing terms of the playout frameworks?

Can I use Microsoft's open source Silverlight Media Framework as a basis for creating a Smooth Streaming player?

The Silverlight Media Framework is licensed under the Microsoft Public License (Ms-PL).

Please note that the IIS Smooth Streaming Client 1.1 comes with a specific line in the EULA:

1.    INSTALLATION AND USE RIGHTS. You may install and use any number of copies of the
      software on your devices for your use solely with Microsoft IIS Media Services.

So you may have to create your own Smooth Streaming client, or ask Microsoft to lift the restriction, or decide to use another play-out platform like Flash.

Can I use Adobe's Open Source Media Framework as a basis for creating an HTTP Dynamic Streaming player?

Please review the Open Source Media Framework License.