A flame-retardant flexible polymer composition includes a polymer component that contains 98 to 80 parts by mass of a chlorinated polyethylene and 2 to 20 parts by mass of a polyolefin polymer; and calcium hydroxide particles having a surface containing calcium silicate, wherein a content of the particles relative to 100 parts by mass of the polymer component is 5 parts by mass or more and 20 parts by mass or less. A polymer tube is formed from the flame-retardant flexible polymer composition. An insulated wire includes an insulation formed from the flame-retardant flexible polymer composition.