A process for the production of a flame-retardant polymer is disclosed. The process includes reacting a triol with an organophosphate monochloride material to produce a phosphorus-functionalized hydroxyl material. The process further includes reacting the phosphorus-functionalized hydroxyl material with a polycarboxylic acid to form the flame-retardant polymer. Phosphorus is chemically bound to a polymer chain of the flame-retardant polymer.