Assuming you are talking about an actual award booking, and not Amex Pay With Miles program (as noted above, Amex Pay With Miles option is only available on itins that are 100% DL metal).

For award bookings, since the last segment is flown by a partner, an award will require DL Skymiles award availability on the partner operated flight. Partners do not offer award space to DL on every single flight. Married segment availability can come into play as well, but that does not seem to be the case here as KL has simply not released any award inventory on the KL operated flight to DL for Skymiles redemptions.

On 100% Delta operated itins, DL has multiple Skymiles award classes on each flight with different mileage amounts -- for Main awards it is NY/NB/NM/NH/NQ/NK/NL/NU/NT/NX/NV which are analogous to the Main revenue fare classes, but without the 'N' prefix (although bucket inventory availaibility in the classes isn't always an exact match on any given flight). So generally speaking, if you can book a revenue fare on the flights, you can also book a Skymiles award on them (albeit at potentially very high mileage amounts if revenue fares are also high due to limited inventory in lower classes or high demand periods).

For partner operated flights, award availability is entirely binary as there is only a single partner award class for each cabin (and it is not unusual for the value in that bucket class to be a zero for Skymiles redemptions).