Two types of nitrogen-doped carbon nanomaterials embedded with novel transition metal-based medium entropy alloy nanoparticles are synthesized via a simple, scalable, and cost-effective single-step pyrolysis route, by varying the stoichiometric ratio of iron and cobalt. The samples predominantly have bamboo-shaped nanotube morphology with some globular structures. The globules are core-shell type nanoparticles, i.e., containing the metallic-alloy nanoparticles encapsulated by the graphitic shell and embedded within defective amorphous-type carbon matrix. The electrochemical studies using these samples are conducted in basic medium to explore their potential for Zn-air batteries. Electrochemical measurements are carried out in 1 M and 0.1 M KOH, respectively, on a rotating disk electrode setup. The sample with higher cobalt content performs better for both oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) with regards to lower onset potential, lower Tafel slope and lower activation energy. However, the stability towards OER is better for the sample with higher iron content. The sample with higher cobalt content shows a better overall oxygen electrochemistry compared to the one with higher iron content, is at par with several state-of art electrocatalysts and is utilized for fabrication of a prototype Zn-air battery demonstrating its practical applicability.