Development of a versatile method for incorporating conductive materials into textiles could enable advances in wearable electronics and smart textiles. One area of critical importance is the detection of chemicals in the environment for security and industrial process monitoring. Here, the fabrication of a flexible, sensor material based on functionalized multi-walled carbon nanotube (MWNT) films on a porous electrospun fiber mat for real-time detection of a nerve agent simulant is reported. The material is constructed by layer-by-layer (LbL) assembly of MWNTs with opposite charges, creating multilayer films of MWNTs without binder. The vacuum-assisted spray-LbL process enables conformal coatings of nanostructured MWNT films on individual electrospun fibers throughout the bulk of the mat with controlled loading and electrical conductivity. A thiourea-based receptor is covalently attached to the primary amine groups on the MWNT films to enhance the sensing response to dimethyl methylphosphonate (DMMP), a simulant for sarin nerve agent. Chemiresistive sensors based on the engineered textiles display reversible responses and detection limits for DMMP as low as 10 ppb in the aqueous phase and 5 ppm in the vapor phase. This fabrication technique provides a versatile and easily scalable strategy for incorporating conformal MWNT films into three-dimensional substrates for numerous applications.