Well this make it a little harder to diagnose, since I cannot see it firsthand. I would verify that the tank has absolutely stopped filling, because this is a typical noise that occurs especially when the fill valve is completing the fill.
If there is no supply water moving at the time of the noise, then I would have to guess that it is in the drain piping. I would look for any areas where the piping may be rubbing against something, as the water drains. If you have a basement or crawlspace, have someone down there to listen while the toilet gets flushed.
Once the toilet fills and the fill valve shuts off, this sudden stop can cause vibrations to be sent back thru the supply lines. This can cause water hammer, in which a water hammer arrester would help to fix the problem. The supply piping could also be loose and hitting something nearby. It would be good to verify that all piping is adequately secured to the framing. A water hammer arrester is shown below; it reduces the shocwave sent out by the sudden stop of water.
If you need further help or clarification on this answer, please do not hesitate to reply to this post.
Thanks for asking your question at Just Answer.
Best of Luck, Brian
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