Briefly:

cd /usr/local/FlashphonerWebCallServer/bin
./shutdown.sh
./startup.sh

With diagnostic commands:

1) cd /usr/local/FlashphonerWebCallServer/bin

2) ./shutdown.sh

#Just to be sure that Flashphoner process is properly stopped
3) ps aux | grep Flashphoner

4) ./startup.sh

#Make sure the server is restarted and logs are
5) tail -f /usr/local/FlashphonerWebCallServer/logs/flashphoner.log

#Make sure the Flashphoner process is alive.
6) ps aux | grep Flashphoner

Steps 3,5,6 are optional.