“How long does a kidney infection last without treatment?”

Can't tell for sure. It may resolve in 1-2 weeks on its own if you are super healthy and drinking lots of fluid, but may not go away, and in that case, you would need antibiotics. Also, did you have symptoms of urine infection? or the infection was simply discovered on urine testing and the doctor told you that you have an infection. The latter could be an asymptomatic infection, and its treatment is a judgment call. But if you had symptoms of UTI, best to treat.