Also you can try add an initscript.
Create a new script in
sudo vim /etc/init.d/myscript
(Obviously it doesn't have to be called "myscript".) In this script, do whatever you want to do. Perhaps just run the script you mentioned.
java -jar /path/to/jenkins.war &
Make it executable.
chmod ugo+x /etc/init.d/myscript
Configure the init system to run this script at startup.
update-rc.d myscript defaults