In case the above solution doesn't work for you, use ssh to login to your server, move to the root directory of your unpacked flyspray sources and execute this:
curl -sS https://getcomposer.org/installer | php php composer.phar install
If you are on a shared hosting, there are probably different php versions available. The hosting companies name them often like php5.4, php5.5-cli or php-cgi-7.0. Choose the best matching php-version for your Hosting (should ideally match that of what the webserver uses). To see available php versions on the commandline type
php tab tab
tab tab is autocompletion on bash, so it shows all executable that start with php.
Lets say the webserver uses PHP 5.6 by default, than a php5.6 you found on the commandline is a good choice:
curl -sS https://getcomposer.org/installer | php5.6 php5.6 composer.phar install
Or take an official release, which contains all needed external packages bundled.