The proper way would be to measure the new windows to fit inside the existing frame. Sounds like you already ordered them to replace the whole frame though. Theres no way of getting around it you'll need to use the flange. If you have casings around the windows or vinyl siding it will be a pretty easy job.

Thanks for your response.

I'm having new siding put on, but unfortunately, it may not be that easy, the outside is going to have the original 7/8" Masonite siding, new 1/4" insulation and the new 7/8" siding...I suppose I'll try my best to build the jambs out.

Again, thanks.

Since your doing siding you will be able to get away with leaving the fin off. Just seal the window against the old siding, you'll want to use 100% silicone and run a good size bead all the way around. That along with having new siding over it the window will never leak. Sorry about the confusion.