Materials with transition metals in triangular lattices are of great interest for their potential combination of exotic magnetism and electronic topology. Kagome nets, also known as trihexagonal, are of particular importance since the discovery of geometrically frustrated magnetism and massive Dirac fermions in crystals like Herbertsmithite and $mathrm{Fe_3Sn_2}$, respectively. Recently, $mathrm{K_{1-x}V_3Sb_5}$, was discovered to be a layered, topological metal with a Kagome net of vanadium, and shown to have a giant extrinsic anomalous Hall effect (AHE) related to its triangular lattice. Here, we fabricated Josephson Junctions (JJ) of $mathrm{K_{1-x}V_3Sb_5}$ and induced superconductivity over extremely long junction lengths (6 $mathrm{mu m}$). Surprisingly, through magnetoresistance and current vs. phase measurements, we observed evidence of both spin-triplet supercurrent and spatially localized conducting channels arising from topological edge states. This observation opens the door to studying the interplay of quantum magnetism, strong correlation, and topology as well as facile generation of spin-triplet supercurrent for quantum device applications.