A little bit of background. Portal for ArcGIS is federated with ArcGIS Server with Web Tier (IWA Authentication). Application consuming REST Services is ASP.Net.
I don't think I can use the OAuth protocol. The consuming application is based on ASP.NET. Here's an example request for obtaining Legend of a map
Each Time I get 302 HTTP error code since it does not have token info. When I open a separate window it does resolve since I've access to this content.
302 HTTP status codes aren't usually associated with a token issue. There may be something else going on here. I'd suggest contacting Esri Support Services so an analyst can take a closer look.