As you're talking about an affinity group I'm assuming you're using a database server on a Virtual Machine.
Traffic costs only apply when sending data out of the data centre, so irrespective of whether the servers are on the same affinity group or not you will not incur data transfer costs as long as you deploy everything to the same Windows Azure dada centre.
If you deployed all the virtual machines on the same virtual network they will simply see each other on the network.
Another option, which does not require the servers being on the same network (or even on the same account), when using SQL Server, is to export the database to blob storage and import it on the other server.
This would also be the mechanism I would use if you were using Windows Azure SQL Database