If you are getting creative with ITA Matrix, this is also a good website to know about, since some ITA Matrix itineraries can otherwise be hard to book:

https://bookwithmatrix.com/

Whichever site you ultimately book with should let you put in a frequent flyer number, but there can be some weird outcomes -- for example Book With Matrix may actually let you book a ticket on Delta.com for airlines where it is not possible to earn any Delta miles. So be careful.

The links provided above to the lists of Delta's partners are a good place to start. The airline that appears in the flight number is what counts for how many miles you earn (for example AF6789 is an Air France flight number but might actually be a flight operated by Delta -- in which case you check in with Delta and fly on a Delta plane but you earn miles as though it was an Air France flight).

But be aware that if you book a flight on a partner flight number, but it is operated by an airline that is not a Delta partner, you generally won't earn any Delta miles. For example Air France has a partnership with Japan Airlines but Delta does not, so an Air France flight number on a Japan Airlines-operated flight would not earn any miles.