The Dropbox API does have a general rate limiting system, but note that not all 429s and 503s 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.
For example, if you're making multiple changes at the same time in the same account or shared folder, you can run in to that 'too_many_write_operations' error, which is "lock contention". That's not explicit rate limiting, but rather a result of how Dropbox works on the backend. This is a technical inability to make a modification in the account or shared folder at the time of the API call. This error indicates that there was simultaneous activity in the account or shared folder preventing your app from making the state-modifying call (e.g., adding, editing, moving, or deleting files/folders) it is attempting. The simultaneous activity could be coming from your app itself, or elsewhere, e.g., from the user's desktop client. It can come from the same user, or another member of a shared folder. You can find more information about lock contention here:
https://www.dropbox.com/developers/reference/data-ingress-guide
In short, to avoid this error, you should avoid making multiple concurrent state modifications. E.g., don't issue multiple such requests at a time, and use batch endpoints whenever possible. That won't guarantee that you won't run in to this error though, as contention can still come from other sources.
