The Dropbox API does have a rate limiting system, but we don't have any specific numbers for the allowed rates available.
Note that not all responses with a 429 and 503 status code indicate explicit rate limiting, but in any case that you get a 429 or 503 the best practice is to retry the request, respecting the Retry-After header if given in the response, or using an exponential back-off, if not.
