A process for the production of a flame-retardant polymer is disclosed. The process includes reacting a polyol, for example glycerol, with an organophosphorus monochloride material to produce a phosphorus-functionalized polyol derivative. The process further includes reacting the phosphorus-functionalized polyol derivative with a polycarboxylic acid to form the flame-retardant polymer, wherein phosphorus is chemically bound to a polymer chain of the flame-retardant polymer.