Your grep is getting the output of find piped into it, so there's nothing in the find command itself (which has the -exec in there) to filter it down so it applies to everything find finds. You're filtering for 'Aug 18' after find has already -exec the cp -ltr command.

You probably want this:

find . -name '*-FLAIR' -name '*Aug 18*' -type d -ls -exec cp -lr -t ../../../media_links/ {} \;