2CDSD 2C,
Unfortunatly, the Esri Resource proxy does not support printing secured services at this point. I have done some digging and found (from PrintTask, Secure AGS Service, and Resource Proxy ) this:
The resource proxy will not print a secured map service. This is by design. So it is possible to use the proxy in order to authenticate and display the secured service on the map, but when it comes to printing a secured service, the resource proxy will not handle this scenario as it will not pass the token in the Web_Map_as_JSON parameter. If you are using a short lived token, then a solution would be to let the identity manager handle the authentication for you, meaning that you will get a prompt to enter your credentials once the app loads and then these credentials will be used when you try to print. Otherwise, you can create a custom print service and embed the credentials as described in the article. If you choose to use the second option, please make sure that you use a 10.3 print service or above as there was an issue in the earlier versions which is fixed in 10.3
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I have spent about a month on the phone with Esri tech support about this and have spoken with ArcGIS Server and Online personnel at the Esri UC this past summer and have gotten the same answers. Because the proxy won't apply the token it has, the print service will then not have permission to access the secured layer. I have tried and gotten the same errors as you are seeing.
(My GeoNet thread: https://community.esri.com/message/598929 )
The suggested action by Esri tech support and the Esri staff at the UC was to custom edit the proxy to apply the token to the request.
Sorry about the bad news.
Chris