If you get caught near a tornado while traveling on the road and you can't avoid it, get out of your vehicle into the closest building and stay away from windows. A couple of months ago near OKC, customers were gathered in a convience store's walk-in cooler. The store took a direct hit, but there were no injuries.
If there is not a building close by, lie down in a low area such as a ditch. It won't be fun, but it's better than staying in your vehicle. If at all possible, cover yourself with blankets or something similar for protection from flying debris.
Most campgrounds do not have a storm shelter, so try to take cover in the campgrounds bathhouse. You may have less than a minute to get to safety, so be prepared. Stay tuned to local radio and TV stations if threatening weather is close by.
You really don't need to worry too much. While tornados can and do occur through out the year, the height of tornado season for Kansas/Oklahoma/Texas has past, April - June.
You will experience hot and humid weather, temps in the high 90's - low 100's with heat indexs as high as 110. Storms can build in the heat of the afternoon, 10-20% chance, and most only produce rain. Some can contain hail and lightening but tornados are rare with these types of storms. However, the storms can fall apart quickly and produce micro bursts. Straight line winds as high as 70 or 80 mph. They can turn a trailer over but again this would be a rare occurance.
You truley have a very slim chance of experincing any of the bad weather conditions I mentioned above, so relax and enjoy your trip.
Good luck and happy camping!