Eating foods not on the suggested FAA food plan (even if they don't have sugar/flour/wheat in them) can cause cravings. Foods not on the plan like this are called "gray foods" and eating them is dangerous because it can lead the abstinent food addict back into active addiction. Some examples of foods like this are cheese, potato chips, popcorn (with or without butter), cream, butter, etc. Notice that these are all high-fat foods. Many food addicts are addicted to not only s/f/w, but also to high-fat.
There are also certain high-carbohydrate foods not on the FAA suggested food plan because they trigger cravings in food addicts. Some examples of these are bananas and mangoes.
Also, there are food items on the suggested FAA food plan that might be personal trigger foods for certain individuals but are OK for other abstinent food addicts. For instance, I myself found after following the food plan for a while that I needed to let go of rice cakes. As long as I was at it, I also let go of the puffed cereals because they have hardly any fiber. I'd prefer to eat high-quality foods with fiber because fiber gives us the feeling of being full and satiated... and that feeling helps us get from one meal to the other without hunger. Some other foods I've heard abstinent FAA members had trouble with and gave up for their well-being are grapes, cherries, corn. Some can't eat watermelon. We're all different and have to find what works for us within the parameters of the food plan.
Finding your personal trigger foods (they "trigger" cravings in you) takes some experimenting, and I suggest working with your sponsor on this... at least that's what I did and it was a huge help. As you're probably also finding, clean abstinence is going to take "H.O.W." = honesty, open mindedness, and willingness. Some people are able to come to FAA and find this from their first day, other FAA members don't "get it" immediately and achieving clean abstinence is more of a process for them. Whichever type of person you are, you are very welcome in FAA and we're glad you're here. Don't eat s/f/w, go to meetings, and ask for help. FAA does work!