Q.growing tomatoes in a plastic 5-gal. bucket
I have fall tomato plants growing in Louisiana on my concrete driveway (the only place I have enough sun during the day). I have the buckets w/holes drilled on the bottom of the buckets and sitting on 1×6 boards with about a 6″ gap between the boards. We have rain forecast for the next several days. Do I need to take them out of the rain for a few days? Will too much rain damage or ruin the plants? They are only about 8-10 inches tall now.

If you have heavy rains coming and the plants can be moved, you can certainly move them to a sheltered location to lessen the risk of your plants being overwhelmed or stressed with excess water.
If you are unable to move them just make sure the excess moisture is draining freely from you containers. It is wise to rise the pots up from a flat surface as you have done.