Hello @itpurchasing_0730,
It sounds like you set things up correctly, but seems like Chocolatey is behaving strangely; if you added a source, then you shouldn't be prompted for the credentials.
In general, you should just need to run choco source add command:
https://docs.chocolatey.org/en-us/choco/commands/sources
Then you won't be prompted again. I would try removing your sources, and adding them back.
You may also want to use a tool like Fiddler classic to monitor the traffic that Chocolatey is making. Unfortunately we can't tell, from just that diagnostic log.
That will let you see exactly what URls are being used... and the underlying problem might be related to something like a proxy server.
Cheers,
Alana