A high-strength, lightweight inflatable structure is formed of at least one flexible fabric member that, in an inflated condition, forms a self-supporting structure. The flexible fabric member is formed from a bare fabric having an areal weight of less than 4.5 oz/yd2. The fabric is coated with air-impervious resin coating comprising a polyurethane resin having a mixture of graphene nanoplatelets and a phosphorus-based flame retardant added thereto. The thermally exfoliated graphene nanoplatelets contain residual graphene oxide. Graphene oxide, which is a polar molecule, has an affinity for the polar molecules that make up the phosphorus based flame retardant. Accordingly, in addition to its inherent flame-retardant properties, the phosphorus based flame retardant acts as a dispersant to improve the uniform dispersion of the graphene nanoplatelets within the matrix, thus reducing or eliminating the need to use additional dispersants.