Fly ash (FA), an abundant waste from thermal power plants in Vietnam, has been recycled 100 % into multi-functional aerogel composites for heat and sound insulation by the green fabrication developed in this study. The hollow structure of aerogel composites is created by sublimation of water in a mixture of FA and recycled polyethylene terephthalate (rPET) fibers bound by environmentally friendly adhesives including polyvinyl alcohol (PVA) and xanthan gum (XG). As result, the FA/rPET aerogel composites exhibit an exceedingly low density of 0.045 - 0.060 g/cm3 and high porosity of 94.81 - 97.02 %. The aerogel composites have a low thermal conductivity of 0.035 - 0.040 W/(m·K), a comparably high noise reduction coefficient (NRC) of 0.49, and a high working temperature of 220 °C. The prepared FA/rPET aerogel composites display the ability to slow down the burning in the presence of FA at 3.0 wt% with a burning rate of 1.0 mm/s and extinguish the flame only 30 s. The effect of FA content on the morphology, physical and mechanical properties as well as thermal conductivity, acoustic insulation, and slow-burning of the aerogel composites is also investigated comprehensively. The features of slow-burning aerogel composites from FA and rPET fibers such as lightweight, flexibility, thermal and sound insulation give them great potential in civil engineering towards a green approach and sustainable development.