If the core is not damaged this is how I would do it.
Take a fly tying bobbin and cover the spot with thread over the spot and a quarter inch on each side. You Spin the bobbing around the line, holding the fly line in your hands using your thumb nails to guide the wraps. If you do a good job the area will just be slightly larger than the diamater of the fly line. Cover with several coats of Pliobond letting each coat dry before the next.
Here is a link
to a post that show you how to make the whipped wraps. Scan down the thread and there is a video that shows the procedure.
The method that I show at the top of the thread to make a loop can also be used to splice two pieces of fly line together. You strip the two ends, upbraid the core, lay them side by side and whip over with thread. Add Pliobond and it is very strong. You will end up with a splice that is about 5/8" long.