Hi @Josh Davis
There are actually two logins you deal with when it comes to reporting services.
The login to the database is to capture the data, it has nothing to do with the actual report itself. That login you used is sent to the database as the user / credentials being used to pull the report data.
This prompt you have a screen shot of, is the authentication to the report server, by default rs uses windows authentication so enter your domain\username with password.
If you do not like this default behavior you can change it, this guide should get you started: http://msdn.microsoft.com/en-us/library/cc281253.aspx
For details infomation ,please refer to :https://stackoverflow.com/questions/12166202/reporting-services-ssrs-prompts-with-username-password
Best Regards,
Isabella