Juliane,
Thanks for your question!
So the good news is that the
Boma - Flavors of Africa restaurant is not in the
Animal Kingdom Park, but actually in
Disney's Animal Kingdom Lodge. So no, you do not need to have a theme park ticket to access the restaurant.
I do strongly suggest you get a reservation, though. When you pull up to the resort gate, you can let them know you have a Boma reservation, and they will direct to where you should park your car. Make sure you go to the Animal Kingdom Lodge - Jambo House, not to Kidani Village, which is nearby, but not where the restaurant is located.
By the way, this is one of my favorite restaurants at Walt Disney World, both for breakfast AND dinner! If you have never been, make sure you give yourself some room on your plate to try some of the amazing Indian- and African-inspired options. My girls, who are not the most adventurous diners in the world, have enjoyed some of the options here that have shown them that having spice in a food does not mean it is going to be hot-spicy necessarily!
Have a Magical (and delicious) Vacation!