To add to the other comments. There is a grammar rule about this, but most native speakers do not give it a second thought. It is called adjective order. We naturally put adjectives in this order: opinion, size, age, shape, color, origin, material, and purpose. That is the reason "The Dragon Boat Festival is a traditional(age) Chinese(origin) festival." sounds more natural. :)

The more natural answer in English is ... a traditional Chinese festival If the conversation was about "traditional festivals" in different parts of the world, then you could refer to the Dragon Boat Festival as a Chinese traditional festival but under most normal circumstances it would be more natural to say 'The Dragon Boat Festival is a traditional Chinese festival'.

Both are perfectly correct. There is no difference in meaning. There may be a tiny difference in emphasis. I'm not sure! It think that "Traditional Chinese festival" emphasizes "traditional," and "Chinese traditional festival" emphasizes "Chinese." Thus perhaps one might write "Eating at Kentucky Fried Chicken on Christmas is a modern Chinese custom. The Dragon Boat Festival is a traditional Chinese custom." and "Ethnic communities in Boston celebrate their traditional festivals. The Dragon Boat Festival is a Chinese traditional festival. Tet is a Vietnamese traditional festival. St. Anthony's Feast is an Italian traditional festival."