The expression km de route does exist in French and Google finds many occurences but Chaiyaphum est à 337 km de route au nord-est de Bangkok is not something I would expect to hear from a native French speaker. What would be more common is: Il y a 337 km de route pour aller de Bangkok à Chaiyaphum but it is difficult to place northeast in this sentence.
Here is what I can suggest:
Chaiyaphum se trouve au nord-est de Bangkok, à 337 km par la route.
This is close to what I found here:
La distance entre Bangkok et Chaiyaphum est de 282 km. La distance par la route est de 337.5 km.