I have just run across your post from seven years ago and I expect your questions have been answered but I will tell you anyway. The Flaten farm is a flat strip of land down by the water and near the church in Vang. Just yesterday I met one of your relatives. He is Robert A. Flaten, the former US Ambassador to Rwanda. He lives in Northfield, MN. By the way, the Flaten farm is quite near the Gaasedelen Farm, now called Steinsvold.
Hope this post finds its way to you,
Jim Gaasedelen