Could this be they walk the dogs? Or would there be a post-position for that sentence?
No. चलते is 'walk' in the sense that the subject is walking. Usually, I would suggest using चलाते like in वे कुत्तों को चलाते हैं for 'They walk the dogs' but that sounds a little weird because चलाना is also used as 'drive' (a vehicle).