This is a known issue, and all depends on who booked the ticket, and in what fare bucket. If you book with KLM, you can select KLM seats on the KLM website, and it will redirect you to Delta.com for the DL flights. However...

• If you are trying to book your upgradable seats based on your KLM status, DL does not allow that until 24 hours prior to departure.
• If you want to just select regular seats on DL, it all depends on your class of booking: KL and DL might be partners in name (and operate under SkyTEAM) but a team they are not. Fare class will determine if DL will allow you to select seats.
• It works the other way around as well: if you booked all under DL, they will only allow you KL seat selection if your class/fare permits it. For some fares, DL will want you to pay for seat assignments, even when flown on KL metal.

I have this very issue right now for a reservation in March which involves two regional DL flights, one transatlantic KL flight and one transatlantic DL flight. Ticket through KLM, and on the KLM flight I was able to select my premium seats without any problem. DL is allowing me only basic seat selection, and upgrades can only be selected 24 hrs before the flight. If my return flight had been on a KL tube, I would have been able to select my premium econ seat with no problem. This lack or reciprocation and alignment between KL and DL is shameful... and totally unnecessary. It is, of course, all about the money and not customer convenience or recognition...