Yes, but Flying Blue is not an airline. Hence, your programme number can be associated freely with any/all of: Air France, KLM, Kenya Airways, TAROM, AirCalin (though not all of these options will always be offered)

The "norm" is that each airline has its own programme, so when you are invited to enter your frequent flyer details, the options are most often presented/listed by airline rather than by frequent flyer programme. Sometimes it's a combination of both (i.e "Air France Flying Blue/Delta Skymiles/Alitalia Millemigilia/KLM Flying Blue etc ).

Internally, your 10-digit Flying Blue number can be preceded by either "AF" or "KL" (and, presumably, KQ, RO, or SB), as you will see on some of your e-tickets. Here are some samples of mine, both showing my Flying Blue number (blanked out), as emailed by Amadeus after schedule changes/cancellations...