Now, have you ever found it annoying that you always have to bring a pokémon with Flash, even though it's a completely useless move with a bad accuracy? Say no more, because I've made a guide to get through the dark part.
The first thing you need to do is to know the way. Just travel through the cave with Flash a few times and you will soon start to memorize how it looks. This will make it easier for you to remember the way when it comes to going without Flash. Do it until you never take a wrong turn and know the way like the back of your hand.
Then, go into the cave again, but don't let the pokémon with Flash (which you should still have if you would get lost in the instructions and get stuck) use Flash this time. Follow the guide below exactly and try to imagine the place where you are at that exact moment, and if you're not in the blue part of the cave when it ends, use Flash to see where you are. You should recognize the place and just go outside again. It can also come in handy to have a pokémon with Dig the first few times, just to be safe.
Go through the cave again and again using the guide, and then it's time to try it without the guide.
When you're trying it without the guide for the first time, be sure to bring your Flashing pokémon. If you get lost, bringing up the guide won't help you. Try to remember where to go next, connecting each move to the place you think you must be on. If you end up in the blue part, then congratulations. If not, just use Flash and see where you are and go through it with the guide again.
Now, you must be getting a little impatient. What you want is to bring your good team to battle Red (Ash) without having one of them to know Flash, right? When you think you're ready, there comes the tricky part. Bring the Flash HM and make sure one of your pokémon can learn Flash. Don't teach it to the pokémon, just bring the HM and go through the cave without the guide. Now, if you get lost, save your game, teach the Flash HM to a pokémon and use Flash. Check carefully where you are, then turn your gameboy off, turn it back on, and the pokémon won't have Flash, but you will know where you are.
So, I hope this guide has helped you and you can bring that super team to fight Red now!