Rescue motors don't come with capacitors. You have to buy it seperatley it should say on the motor box what size cap the motor will need two brown wires
Replacing the flame sensor won't fix your problem. Does your furnace have a circuit board? Does the gas valve have 24 volts across it as it drops out if so replace valve. If 24 volts drops out as flame drops out replace control board. Make sure rollout switches aren't opening.
Do you only have one thermostat either upstairs or down. If so you might want to look into a zoning system where a thermostat would be added so you would have both floors controlled by dampers in the ducts. Can be kinda expensive but it would solve your problem