Free-standing, highly flexible and foldable supercapacitor electrodes were fabricated through the spray-coating assisted layer-by-layer assembly of Ti3C2Tx (MXene) nanoflakes together with multi-walled carbon nanotubes (MWCNTs) on electrospun polycaprolactone (PCL) fiber networks. The open structure of the PCL network and the use of MWCNTs as spacers not only limit the restacking of Ti3C2Tx flakes but also increase the accessible surface of the active materials, facilitating fast diffusion of electrolyte ions within the electrode. Composite electrodes have areal capacitance (30-50 mF cm-2) comparable to other templated electrodes reported in the literature, but showed significantly improved rate performance (14-16% capacitance retention at a scan rate of 100 V s-1). Furthermore, the composite electrodes are flexible and foldable, demonstrating good tolerance against repeated mechanical deformation, including twisting and folding. Therefore, these tens of micron thick fiber electrodes will be attractive for applications in energy storage, electroanalytical chemistry, brain electrodes, electrocatalysis and other fields, where flexible freestanding electrodes with an open and accessible surface are highly desired.