Can a person be more likely to get gangrene from his genetics?

Indirectly Yes. Peripheral vascular disease develops more likely in people who smoke, have diabetes and who are older. There are other factors, but of the top three, diabetes is the one which can be genetically transmitted. Smoking can be controlled. Consult your primary care physician to see if you are at risk for developing diabetes.
No. If there is a genetic predisposition , for diseases like diabetes, atherosclerosis etc neglected care may lead to gangrene of extremities.