The place is hanted and there is no two ways about it. Now sink thread.

Probably not a water hammer.
One possible cause of the noise:
When you flush, cold water runs through the pipe and causes it to contract in length. As the pipe returns to ambient temperature, it tries to expand, but it hangs up somewhere. When it pops loose, you hear it. How much of your plumbing can you lay eyes on?

I can't see much of the plumbing as the toilet is on the 2nd floor. Unfortunately I think most of the pipes are in the walls.
This is starting to sound expensive!