Are you in a detached house? Do you own or rent? Have you contacted a roofer or your original contractor?

How do you know it is coming down the flue?

You may be able to locate the source of the breech by watering the roof when it is dry and seeing exactly where the water is coming in.

There is no way even in a downpour ofs everal hours, that you could get enough water down a flue to "flood your basement.
To see for yourself just how much water could come through the chimney, put 4 inches of water in a 5 gallon bucket....then dump it out on the drive way and see just how much water it is. Then put 1 inch in the bucket, a more moderate amount for even a heavy rain and see how little that is.
Your water is coming from somewhere else.
Linda C

are you sure it is coming from there and not ground water entering thru the walls? maybe your sump pump is not functioning.

Maybe the water is coming down the outside of the flue, because of a flashing or roof defect?

I'm with the flashing / roof defect person. Seen this issue before, started out appearing as rain coming down in chimney, had had a tree fall and thought it damaged the cap on the chimney. Then one toad strangler of a rainy night wall above fireplace developed that oh oh bulge...

Issue was damaged flashing.

Have a good roofer you trust look to be sure.

We had that happen when we had our first good storm after moving into our tract. Lots of people in our tract of a few hundred homes had that problem from the same storm. The builder resolved the problem with a chimney cap and sealing the brick on the chimney and firebox.