I've called the Flying Blue service desk back in November, when I started flying KLM more often. It has been a long phone call, but we figured out that in the one-to-last step of the booking process at the KLM website, you're able to select a specific fare class and you're able to view the rates per class (only checked economy). It was a small link called 'wijzig ticketvoorwaarden' - not sure how this was translated into English.

Since mid December I haven't been able to find the link anymore. Called KLM this time and they told me it disappeared due to a bug on the website. Not sure whether to believe them, since they've been telling me a lot of nonsense in the past months, so @mandatory 's reply here sounds way more logical.