Don't !
I'll answer the actual question in a moment but do yourself a favor, cut off that valve, replace it with a new quarter-turn stop valve and a separate high quality braided supply hose. Just stop reading and go do it. No, really.
The valve is old, it'll need replacement, and I always say with an old valve like this, any time you're crouched down working on it is the best time to replace it. But the real problem is the hose, which is integral to it and cannot be separately replaced! So change both.
The hose, and the washer
That's a corrugated/flex supply pipe/riser. It uses an obsolete kind of compression fitting. You can still buy corrugated risers, but they have modern fittings. All kinds of modern fittings, you can even buy Sharkbite corrugated supply pipes.
Your old pipe does not have a special manufactured end, it just uses a compression fitting similar to the more common metal ferrule/olive that compresses against both the outside of a smooth pipe and the face of a fitting. To do that with a corrugated pipe you use a special rubber washer, either a top-hat shaped Step Washer that grabs the pipe and has a flat face for the fitting, or a Threaded Cone Washer that screws onto the pipe to make contact and mates with the fitting in a wedge shape. If you insist, they're easy to find with those search terms.
Why not
If you are going to make a $200,000 flood insurance claim in the next 5 years, this hose will be the reason. Your valve is old, your hose is old, its construction is obsolete and the special washers are expensive and rarely used. You have a chance now to make this all better. Replace everything.
If you are DIY-ing this, buy a braided hose. There is nothing inherently wrong with flex hoses, but a homeowner can master the braided hose easily, on the first job. Flex ones take a little practice and a failure or two to master. The plumbers who love them have at least overcome that stage. And old-style flex ones with special washers ... nobody is ever going to get to the top of the learning curve with that. Definitely not you. If you fix this and it fails, that will be the first and last time you try it. Just don't.
Instead
Pretty much everything you need: A hack saw, a Sharkbite measure/debur tool, a Sharkbite angle stop with 3/8 compression fitting, and a metal breaided supply hose. Oh, some steel wool and a Sharpie. If you've never done any plumbing before, this is a great starter project, it'll take you an hour. Read the instructions!
