If it still doesn't work once you have verified that you have the htaccess file in place you'll need to get in touch with ampps support and see if they can help.
Then make sure you are copying the htaccess file as well. It's an invisible file by default on mac, so google a way to make that visible.
Alternatively, rename the downloaded and unzipped jamroom directory to "jamroom" and place that in your Applications/AMPPS/www directory overwriting what you have in there.
Not sure then, but if you have a working ampps you should be able to download the jamroom core files and place them in your /Applications/AMPPS/www/jamroom directory (no need to use ftp), create the database using phpmyadmin and then run the installer.