Is it normal to have flooding in basement after radon mitigation system installed?
The radon pipe should be tightly sealed through the basement floor. If that gap you identified goes though the floor, then it should be sealed up because the system is supposed to vent radon from the soil. That opening would prevent that from happening and if you had a lot of rain, you could get water rising up through that gap.

Wait until the basement dries out and then play detective to see if you can determine where the water comes from. If it comes from some other cracks in the walls or floor, they should be sealed up to increase the effectiveness of your radon system and to stop the water seepage.