There is a pressing need to extend the knowledge on the properties of insect protein fractions to boost their use in the food industry. In this study several techno-functional properties of a black soldier fly (Hermetia illucens) protein concentrate (BSFPC) obtained by solubilization and precipitation at pH 4.0–4.3 were investigated and compared with whey protein isolate (WPI), a conventional dairy protein used to stabilize food emulsions. The extraction method applied resulted in a BSFPC with a protein content of 62.44% (Kp factor 5.36) that exhibited comparable or higher values of emulsifying activity and foamability than WPI for the same concentrations, hence, showing the potential for emulsion and foam stabilization. As for the emulsifying properties, the BSFPC (1% and 2%) showed the capacity to stabilize sunflower and lemon oil-in-water emulsions (20%, 30%, and 40% oil fraction) produced by dynamic membranes of tunable pore size (DMTS). It was proved that BSFPC stabilizes sunflower oil-in-water emulsions similarly to WPI, but with a slightly wider droplet size distribution. As for time stability of the sunflower oil emulsions at 25 °C, it was seen that droplet size distribution was maintained for 1% WPI and 2% BSFPC, while for 1% BSFPC there was a slight increase. For lemon oil emulsions, BSFPC showed better emulsifying performance than WPI, which required to be prepared with a pH 7 buffer for lemon oil fractions of 40%, to balance the decrease in the pH caused by the lemon oil water soluble components. The stability of the emulsions was improved when maintained under refrigeration (4 °C) for both BSFPC and WPI. The results of this work point out the feasibility of using BSFPC to stabilize O/W emulsions using a low energy system.