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Some quicky remarks:

a well-behaved API should return specific HTTP codes depending on the outcome, that is:
200 for success, or 201 for resource created. 204 is a possibility for an empty but successful response too but I would not advise using the full panoply available. Just be aware of what codes exist and when to use them.
likewise, use 401/403 for permission issues or authentication errors but here you have the @login_required that should take care of that
accordingly, an error should return a meaningful status code to the client - 400 would be a good candidate for an invalid request
the bottom line, always return an appropriate status code, never return HTTP/200 if the request failed. API calls are routinely automated, and the client will rely on the status code returned by the server to determine if the call was successful or not.
useless variable: u = current_user.id  # 2458017363. You could just write: author_id=current_user.id, instead of author_id=u. u is not an intuitive variable name anyway
I don't understand the logic of generating a random ID in your code, the database backend should generate an incremented record ID for you (simply update your data model). I don't see why you need a random value here...
When you decide to handle certain exceptions like except IntegrityError, you can indeed decide to ignore them or hide them to the client but you should still log them for later review. IntegrityError suggests there is something wrong with your handling of incoming data. It should not happen if data is inspected and sanitized properly.
except Exception is too broad when all you're doing is json.loads. The error that you can expect here should be ValueError. Try submitting empty JSON and malformed JSON to verify.
to sum I don't think you should have resp['error'] and resp['success'], just use the same name in all cases eg: 'response'. It is the status code that will make the difference between success and failure. Whatever you do, the API should respond in a way that is consistent and predictable.