Do you have a Flex 3401? If you know the exact operating wattage let me know because I found two values.
First, I found 900 watts while running. Running the Flex for 1 hour consumes 900 watt/hours of energy or 0.9 kWh.
The second value I found was 10.5 amps, converted to watts would be 120 volt X 10.5 amps = 1,260 watts. Running an hour at this wattage would be 1,260 watt/hours or 1.260 kWh.
I am going to use the larger value to not under estimate the amount. If you want to run for 4 hours at this wattage you would need a battery capable of supplying 4 X 1,260 watt/hours = 5,040watt/hours or 5.040 kWh. You then need to factor efficiency losses, assuming a 90% efficient inverter you would need; 5,040watt/hours/0.90 = 5,600 watt/hours. You also never want to completely deplete any sort of deep cycle battery so you always oversize, typically by 20%. To do so multiply 5,600watt/hours X 1.20 = 6,700 watt/hours or 6.7 kWh.
Now that you know your electrical needs, you need to select a battery. I would recommend NOT using a marine deep cycle battery, while these batteries are made for deep cycle discharge, they are not built for the type of cycling you will be performing. I would recommend a renewable energy deep cycle battery, made exactly for this type of abuse. The marine battery will work but a renewable energy specific battery will have much greater longevity than the marine battery. I would recommend a Trojan Deep Cycle batteries, commonly used in off grid solar, wind, and hydroelectric power systems. So since you would likely be using a 12 volt operating battery you can solve for amp hours needed;
6,700 watt/hours /12 volts = 560 amp/hours needed. Unfortunately, that is A LOT of energy to store and hopefully it is the 900 watt operating wattage (or maybe even less). To store 560 amp/hours you would need multiple Trojan batteries hooked up in parallel (+ to + and - to -). I would recommend a sealed led acid battery or gel type so you do not have to monitor battery acid levels in your vehicle. Lead acids require occasional monitoring and addition of ddH2O or you run the battery dry and ruin it. Using this battery;
31-GEL | Trojan Battery Company
you would need at least 5 of them to run the flex at the above requirements.
Not trying to discourage you from doing this because is a great idea and I have thought about it many times, I know you said space is an issue and you are looking at 4-5 batteries to do the job. You could also wire a charge controller into your car to use your vehicle as an auxiliary generator to supply the additional energy you need. Anything with an electric motor requires a large amount of surge energy to start, so make sure the inverter you select is capable of producing a surge wattage required by the flex, all inverters will have the surge max listed but I could not find the surge max for the flex. Again, I think this a great idea and would love to do it myself if I was a mobile pro not just an enthusiast. Let me know if you have any more questions on this because I'd love to help!
