Are there any issues with running 15A power cords into a 20A outlet and line?
No, not any problem at all.
I am currently using the standard IEC power cords that came with my Rogue Cronus Magnum and VPI Scout 1.1.
After about a month or two listening to the new dedicated branch circuits you could always try an after market PC on Rouge amp.
I would stay with the 15 amp male plug. No need for a 20 amp male plug.
As for the wire size used in a cord with a 15 male plug it can be as small as 16 awg or as big as what ever will fit the male plug and or the IEC female connector.
For the amp I would use a PC with at least 12 gauge wire, conductors. If it was me I with go with 10 gauge wire, conductors.
Before you buy anything I would check and find what other guys are using on Rouge amp. Don't just go out and buy something to see how it sounds.
Just an example, I have an ARC tube amp and it hates shielded cables. A shielded cable sucks the life out of the sound of the amp.