I've used my chase points to purchase several Skyteam flights in the past. Some have been Air France tickets, others have been Alitalia tickets, each time with a DL leg across the pond. For each ticket, when booking, I was unable to enter in my Skymiles number. However, I could use the reference number on Delta's website and enter in my Skymiles number onto the reservation and everything worked out well for me. All other Delta tickets have been purchased directly from Delta.com.

However, I've recently purchased a ticket on China Eastern with no Delta flights on the reservation, and I'm unable to add this ticket to my Skymiles account. Similarly, I've purchased intra-Europe flights on KLM and Air France in the past, and I cannot look up those reservations on Delta.com. However, I've been able to credit the AF and KL flight to DL. I've needed to log onto their respective websites, find the specific reservation, and then add my Skymiles number there. After the flights are flown, the miles are awarded.

If you're wondering about buying a ticket on a random OTA and not adding your Skymiles number at the time of booking, don't worry about it. Assuming it has a Delta flight you do this: Once you have the ticket, you can log into your Skymiles account and look up the reservation using either your ticket number or reference number and adding your Skymiles number. That field is located under "Passenger Information". If you buy an KL, AF, or AZ ticket with no DL flight, then you'll need to use their websites to add it, or wait until after the flight and ask DL to credit you the points.