I recently spoke with legendary studio guitarist "Telecaster" Bob Bain. Beside being a one of the most recorded guitarists in history, one of Bob's first job was playing guitar in Freddie Slack's band in the early 40's. He was friends with many important swing guitars, including Allan Reuss and Les Paul. We only spoke for a couple minutes on the phone, but he invited me to drop by his house to chat some more soon.
Anyway, he confirmed that early electric guitar players used roundwound nickel strings, and that flatwounds did not come on the scene until the 1950's. He alluded to the role of one George Barnes in popularizing them - Bob called him"this guitar player from Chicago, George Barnes." I think he was surprised to hear that I knew exactly who George Barnes was.
Here's an article all about Bob from Vintage Guitar Magazine: http://www.vintageguitar.com/2810/bob-bain/