Run a humidifier in the room where the nylon furniture sits. Static charges increase in dry air, as in arid climates or during winter. Heating a house pulls moisture from the air, increasing static charges. Placing water back in the air with a humidifier can greatly alleviate the problem, reducing or eliminating the static shock.
Cover the nylon chair with a natural-fiber fabric, such as a cotton sheet or throw blanket, or a furniture cover designed for the chair. Synthetic fibers -- such as the nylon in the chair -- pick up static charges far more easily. Placing a cover between the nylon and any clothing should greatly reduce the chance of a static spark, which can occur even when shifting positions in the nylon chair.
Spray the nylon chair with a product designed to help eliminate static cling, such as Static Guard. These types of sprays are designed for use on clothing, making them safe for fabric. The science is fairly simple: While drawing humidity from the air, the chemical components of the spray neutralize electric shock by balancing the positive and negative ions on the fabric.
Rub a dryer sheet -- made to eliminate static cling among clothes rubbing together in a dryer -- over the chair prior to sitting in it. This can eliminate the static charge on the chair, and running the dryer sheet over your clothing can add an additional layer of protection.