Generation of flow is an important aspect in microfluidic applications and generally relies on external pumps or embedded moving mechanical parts which pose distinct limitations and protocols on the use of microfluidic systems. A possible approach to avoid moving mechanical parts is to generate flow by changing some selected property or structure of the fluid. In fluids with internal orientational order such as nematic liquid crystals, this process of flow generation is known as the backflow effect. In this article, we demonstrate the contact-free generation of microfluidic material flows in nematic fluids -including directed contact-free pumping- by external electric and optical fields based on the dynamic backflow coupling between nematic order and material flow. Using numerical modelling, we design efficient shaping and driving of the backflow-generated material flow using spatial profiles and time modulations of electric fields with oscillating amplitude, rotating electric fields and optical fields. Particularly, we demonstrate how such periodic external fields generate efficient net average nematic flows through a microfluidic channel, that avoid usual invariance under time-reversal limitations. We show that a laser beam with rotating linear polarization can create a vortex-like flow structure and can act as a local flow pump without moving mechanical parts. The work could be used for advanced microfluidic applications, possibly by creating custom microfluidic pathways without predefined channels based on the adaptivity of an optical set-up, with a far reaching unconventional idea to realize channel-less microfluidics.