Flexsteel is quite commonly used in RVs. Bradd&Hall in Elkhart, IN, has a good sample of Flexsteel seating in their showroom. They also have a web site, http://www.braddandhall.com/, with photos of some of their products.
Villa is another seat manufacturer and Bradd & Hall carries them as well.
A Google search on RV seat will turn up dozens of possible sources, but most shops carry all the same manufacturers.
Have you considered having your existing chair re-upholstered? A local shop should be able to handle that job easily enough and the seat is removable. Just pick out the material you like and leave the seat at the shop.
I'm wanting to have my seats rebuilt and recovered during the this winter while the motorhome will be sitting in the driveway but I am having a lot of trouble finding a shop that will work on motorhome seats. I have told them that I will remove the seats and deliver them but they still will not work on them. They say they work on custom van seats and mine appear to be identical to the Chev. custom van I used to have. Not sure what their problem is but it seems to be universal at least in the Indy area.