Will Oakley bottlecap lenses fit in a flak jacket frame?

No, they will not.

I managed to get mine to fit by marking off how much material to remove off of the bottom and side edges of the lens, masking off the front of the lens, and using a high speed rotary tool w a sanding attachment to actually remove the material. Takes a steady hand and a Dremel.

Also, you have to take just a small amount of material off of the pointed tabs located towards the nose piece on each lens.