That makes no sense. It can be a Platinum charge card or a Platinum credit card but not both. They are very different animals.

The OP does not state where the Amex card he holds was issued. He states that the flight originated in BHX which is in the UK but that is quite a different matter to where the card is issued; I have a flight next week from Vancouver (CXH not YVR) that is insured against a UK-issued Centurion card; nothing to do with Amex in Canada.

Each country's (or sometimes region's) Amex operation has its own insurance coverage issued by insurers in that country or region. Without knowing where the OP's card was issued it is impossible to answer the question in any meaningful way.

The unfortunate events described should be covered in full by the insurance that comes with a UK-domiciled Platinum charge card and the details of the insurance policy are available on the Amex web site at https://www.iplatinum.americanexpres...ryBenefits.pdf.

As to the appalling KLM customer service; well, that does not surprise me one bit.