I applied via the regular online form from Delta. I submitted a screenshot of my Gold card from Iberia, and attached a statement of my account activity from Iberia website (PDF).
14 days later, I received an answer saying that the documents were not sufficient.
I immediately answered, attaching a both side copy of my physical Iberia Card, screenshots of the statement directly from the Iberia website (not the PDF), a copy of the email from Iberia saying that I'm now Gold and a screenshot of the homepage of my Iberia plus account (showing the total number of elite points I have, my current status, since when I'm a member, etc.).
The day after, I received a positive answer and I'm now SkyMiles Gold for 3 months.