Is there any way to copy Avi files out of nested folders into a single folder without having to manually traverse them?

If you have access to the share with a windows box map it to z: 

The you could make a bat file and run it and should work

for /r "z:\name\of\source\" %%x in (*.avi) do move "%%x" "Z:\destination\folder\"

 

I tend to utilise windows search using "*.Avi -sample" then cut and paste the files. I just wondered if there was a way to do it internally.

Just to save creating anther thread for what (presumably) is a simple answer, why is it that when I renmove files from /mnt/user/downloads to /mnt/user/media it ends up creating a media folder on the cache drive even though in unraid the media share is set to never use the cache drive?

That could happen if there is a downloads folder on the cache drive.   You are working at the Linux level which does not know about user shares.   I believe that the Linux ‘mv’ command first tries a rename and only if that fails carries out a copy/delete action.