Update... I still can't log in during the check-in process (the button is there, but it won't do anything)

Logging into Flying Blue and then using the menu to get to the main klm.com site seems to be hit and miss - it works some of the time but not all of the time.

I tried to talk to KLM about this via WhatsApp but they were totally useless - first reply was about clearing my cache (fair enough, but it didn't work), they then replied to my follow-up by sending me a long essay about how to retro-claim miles, I wrote back suggesting that they picked the wrong boiler-plate reply but heard nothing further. Waste of time!