You can make a gaming chair with a joystick mount reality with adapters such as Monstertech’s Hotas Chair Mount. Compared to desk-mounted alternatives, having them in easy reach on the gaming chair is best for added comfort.
Solutions such as the one developed by Monstertech or the Playseat Air Force are true options for more realistic simulator experiences. If you already have a gaming chair, you’ll be able to install it on your own, in about 20-30 minutes.