Don't do this.
If you want to know how double jump is programmed, and how to design levels for it, you should play platformers. For example, MegaMan. I strongly suggest you play any MegaMan that has a double jump type of ability, of which there are quite a few. And any that use wall climb, as playing both will teach you about the importance of spatial awareness and level design in a platformer. Also, play Halo 5. I realize a lot of people don't like the new mechanics (because they don't play like a classic Halo game, and I agree), but they are VERY solid, and are a good reference for these things.
Remember, all of your abilities as a player are tools to interact with the world around you. If a player falls, then jumps again, that will extend the reach of a jump they might not have otherwise made. Additionally, you could add a ceiling and wall that covers a hole in the floor, where the player must fall, and use double jump to the right to avoid a pit of spikes below. This is a common little design that you'll find often in platformers, it will become second nature to some.
It being second nature, though, is why it's so important to get it right. Making such a big change must be clearly defined, and have a clear reason for existing.
Take Blitz Breaker (https://www.scirra.com/arcade/action-games/blitz-breaker-demo-3167) for example. This game doesn't allow you to run, and instead vault anywhere at anytime. It's a neat way to set up mechanics, is clearly defined and easy to grasp, and feels like it really makes the experience original and fun.