With Skyteam miles are earned/credited based on the flight number/codeshare, and specifically
not based on the operating carrier. Whereas Star Alliance does it the other way around and only uses the operating carrier for earning purposes.
This means that you would earn according to the flight number on your ticket. So if the flight has an AS Alaska flight number, you would earn according to the earning rules for Alaska Airlines. And unfortunately, Alaska is not a Flying Blue (nor Skyteam) member or partner - meaning zero earnings on that.
So in this specific case I guess the important question would be: What are the flight numbers on your ticket? Are they AS or JL?
Edit: Re-reading your question makes me believe that perhaps the flights were JL coded but FB is denying because JL is not in Skyteam, and the flights were booked through a non-Skyteam partner. That does sound like a familiar rule, though
looking at the JL earning page I do not see that mentioned anywhere. The only limitations specifically mentioned are these:
Earn Miles and gain XP on flights marketed as Japan Airlines (JL), Japan Trans Ocean (NU) and operated by Japan Airlines, Air France, J-Air, Japan Air Commuter or Hokkaido Air Commuter as per the earning scheme below.
Earning Miles isn’t possible for:
- Tickets with a booking class not mentioned in the earning scheme below
- Reward tickets (tickets booked using Miles)
- Flights between France and Japan, using a ticket with one of the following booking classes: H, K, L, M, V, S, O, G, Q, N
I do believe this rule was discussed on this board when FB started allowing earning on non-Skyteam partners, though personally I have never come across this situation. You are sure though that non of the other exclusion rules mentioned above apply to you? If they do not I would consider referring FB back to this link and requesting the credit based on the rules described there.