Back fires and stalls out

Just bought this car all original, Changed out the fan, water hose, belt, Have a new master brake cylinder going in. No parts where ever replaced, Took off all the original parts I replaced. Flush the radiator.

My question is, It back fires and dies out but starts right back up and runs fine except for this problem. It does not do it all the time. But once it did it to me. I am scared to drive the car.

Thanks in advance if you can give me some idea on what may be causing this.
My friend who is working on this car is a retired mechanic of over thirty years.