I second tlr - and what you have copy-pasted from the FB website. If you are flying on a flight - no matter who is operating it - with a ticket that has an AF or KL number, you will get both level and award miles (the number of which will depend on your ticket class). So you should get your maileage credit - call KLM
Please do let us know if you are having trouble getting these credits. It would be interesting for all of us to find out.
Aurelien