make rsync ignore directory structure?
 

Is there a way to force rsync to not make directories in its destination directory; ie, to simply dump all of the files from the source directory directly into the destination without copying any of the folders that the files were originally in?

I tried --no-dirs, but that seems to only be for empty directories.

You will need to specify each file separatally. perhaps.

find directory -type f -print0 | xargs -I@ rsync @ destination/

You can speed this up by replacing xargs with something like parellel
or doing some extra handling of arguments. EG

find ... | xargs -- sh -c 'rsync "$@" destination' 'ss'

The 'ss' is needed otherwise the first argument will become $0 and not $1