I am in a very similar situation as the OP. I bought a KLM Light Economy ticket (FB Platinum give free seat selction etc.) for LHR-AMS-BKK departing on 4th April for just under 800GBP. Buying a KLM ticket in February might seem risky but this was a replacement for my original LHR-BKK ticket I purchased in October 2019 with XiamenAir (MF) via AMS and XMN. When the covid-19 news started hitting the airwaves I got a refund from XiamenAir to avoid potential transit in China problems - little knowing at the time this situation would be as it is today.

Are KLM actually declaring flights to be cancelled? AFAIK, that is the only way to get a refund. So far my ticket is still listed as scheduled.

Likewise, I have a Korean Air January purchased non-refundable business class ticket for LHR-ICN-MNL in May. Still do not know how KE are going to treat this.

Not to mention the 6 hotel reservations I am trying to cancel and get refunded, with no responses from booking.com and pointshound (both via the Flying Blue partners website).