Yes, polyester is flammable.
More Info: Natural cellulose fibers such as cotton and linen are the most hazardous fabrics in terms of burning characteristics. Manufactured cellulose fibers such as acetate and rayon are slightly less. Synthetic fibers such as polyester behave differently when they burn. They are flammable, but they generally burn slowly and melt.
What Are Flame Resistant Fabrics?
Most natural and synthetic fibers used in clothing will burn under the right conditions. Flame resistant fabrics, also called flame retardant fabrics, are specially manufactured and sometimes treated to burn slowly, are harder to ignite, or self-extinguish when the source of the flame is removed. If a product is labeled as /R-flame resistant S then the product is designed to self-extinguish when the source of the heat is removed.
Understanding Clothing Flammability Labels
Flammability clothing standards fall under the jurisdiction of the Consumer Product Safety Commission. Fabrics that are to be used in clothing must meet certain flammability criteria.
Fireproof: The textile will not burn.
Non-combustible: The textile will not burn.
Non-flammable: The textile will not burn.
Fire/Flame-retardant: The textile will be slower to ignite, slower to burn, and may self-extinguish when the flame/heat source is removed.
Fire/Flame-resistant: The textile will be slower to ignite, slower to burn, and may self-extinguish when the flame/heat source is removed.
Combustible: The textile will burn readily.
Flammable: The textile will burn readily.
Inflammable: The textile will burn readily.
Generally, if a textile does not have a flammability resistance label you can assume it will ignite easily.