That time you had a leading / which makes it absolute - for an absolute path it's probably '/home/rbawden/Desktop/install_flash_player_9_linux.tar.gz' (or, as mentioned, '~/Desktop/install_flash_player_9_linux.tar.gz' as long as the tilde expands correctly) and for a relative path, it'd just be 'Desktop/install_flash_player_9_linux.tar.gz'
-- Let me try to do better.
Arow's original post was correct, except that, if you run the command as root, '~' expands to /root/blah and doesn't work. If you run it as normal user (which is what Arow was assuming) then '~' expands to /home/USER/blah. So I wasn't saying to leave of the tilde (which results in a non-existent absolute path) - only saying that the tilde expands relative to the user using it. HTH.