How long can a car run without transmission fluid is up to about 10 miles on low to no transmission fluid, but doing so would be extremely risky.
Transmission fluid is essential for helping your car shift gears smoothly. Without it, gears are exposed to added friction and may not be able to move at all. Driving your car without transmission fluid, or with low fluid levels, is something you should never do if you can help it.
Not only does the reduced handling ability make it more dangerous, but it could also cause extensive—and expensive!—damage to your vehicle.