The full answer
Yes — traditional Play-Doh contains wheat flour
Standard Play-Doh is made with wheat flour as a primary ingredient, which is a real consideration for children with celiac disease, since young children often put their hands in their mouths during and after play.
Gluten-free alternatives exist
Several gluten-free modeling compound alternatives are available and widely sold specifically for this reason — worth keeping in mind for schools and childcare settings as well as at home.
Important context
Individual symptoms, reactions, medical histories, food products, and local labeling rules can vary. Community experiences are not medical evidence.
For personal medical decisions, diagnosis, testing, or treatment, consult a qualified healthcare professional.