Dear Josje, Greek cuisine includes a lot of fresh vegetables and many dishes with legumes and lean meat as well as fish. You should as always pay attention to packed foods and check for the gluten free indication. Mediterranean cuisine, at least as it used to be, traditionally mostly contains little gluten or none.
I think that you have to be careful with the ingredients of bread, just because flour as you may already know, is highly suspicious for gluten residues. Also you should not trust delicatessen food of unknown origin.
I would suggest you do your food shopping in a reliable super market brand and always check the ingredients. I suppose you will be fine, you dont have to worry