Art. 12(3) GDPR explains that an answer to such a request can take up to a month:
- The controller shall provide information on action taken on a request under Articles 15 to 22 to the data subject without undue delay and in any event within one month of receipt of the request.
And Art 12(5) GDPR explains that repetitive can be refuses:
Information provided under Articles 13 and 14 and any communication and any actions taken under Articles 15 to 22 and 34 shall be provided free of charge. Where requests from a data subject are manifestly unfounded or excessive, in particular because of their repetitive character, the controller may either:
(a) charge a reasonable fee taking into account the administrative costs of providing the information or communication or taking the action requested; or
(b) refuse to act on the request.
The controller shall bear the burden of demonstrating the manifestly unfounded or excessive character of the request.
So these articles suggest that such a request is only for existing data at the moment of the request. You could make repetitive requests, but you might have to pay a fee, or it can be refused.
So I don't see how the GDPR would give you a right for transfer of future data.