Well, first of all you will need to go to the manager and express an intrest in volunterring there. You culd suggest you show them what you can do and show them you skills and what you are capable...
I dont know about food banks, but I know that a lot of soup kitchens allow 13 year olds to volunteer. I'm way older than you but i work at a soup every month. It's a lot of fun!
If you want to start a soup kitchen, you could always try at your own home and get at least a lot ingredients for your soups and at least hire some chefs or you could do a family soup kitchen is...