Do oat flakes (Spar S-budget) contain gluten?
This is a situation similar to what consumers with food allergies face - the critical substance is not in the food items per se, but cross-contamination may be a problem.

Oats are gluten-free1, but during processing and packaging, residue of e.g. wheat may get mixed in with the oat. While this is probably minimal and not a problem for consumers who avoid gluten as a dietary choice, the effects on someone with a medical condition may be different - but this is difficult to quantify generally. Some brands offer oatmeal that is certified gluten-free, with the higher effort reflected in the price. 

The only reliable answer for your question can be obtained by asking the manufacturer and whether the possibility of contamination is a problem for you and your body should be clarified with your healthcare provider. We don’t offer medical advice, for many reasons. For everyone who just wants to avoid gluten for non-medical reasons, they should have no problem with this product.