The coffee bean does not contain gluten, a protein which is found in the cereals wheat, barley and rye.
But when it comes to buying and drinking different types of coffee products, care must be taken to avoid traces of gluten spoiling your favourite rousing cup. Flavoured coffees can create issues, creamers could contain gluten, and cross-contamination in the facilities where coffee is ground and processed is not unknown.
In short, coffee is usually gluten free, and, with due care, you should be able to enjoy a caffeine hit in any of its typical forms, whether you are a flat white fan or a cappuccino devotee.