How do I get to the flying gym to beat the gym leader?

Well after you beat the Ground Type Gym leader you need to head to Chargestone Cave. You get there by going left after you exit out of the Ground Gym. Once you get on the Route just follow it to the end where the cave is. From there it's really a straight shot through the cave. After you've ran into your rival and the professor the second time go down and you should see a bridge. The three ninjas will lead to across and talk to you. After this battle the trainer there and go down the stairs. Now follow the path and there will be a split where two guys are standing. Don't go in front of them instead go up the path that leads north. Now turn right and battle the doctor. After the battle he'll heal your Pokemon for you. Now keep going north and you'll see Team Plasma Grunts. After you get to the end of this path lined with Team Plasma Grunts you'll see two staircases. Take the one on the right that goes up. Now follow the path down and to the right. The exit should be right there along with N who will battle you. After battling him head outside and you'll be in the town with the Flying Gym.