Thanks for your thoughtful answer! Indeed, the London flights are for visiting my significant other. However, I need (want) to fly to LHR, as they are not in London but in a town near it and LHR is the closest airport to that place and has, by far, the best bus connection (direct and very high frequency).
Moreover, are you sure about Eurostar being cheaper? I checked tickets and AMS-LON return costs, even several months in advance, are between 150-200€, whereas I usually get a KLM return ticket for 90-100€. I also save on bus prices and about 1h each one-way bus trip by flying to LHR compared to LTN or LGW. I'm more than happy to spend 20-30€ more per flight ticket (effectively only 20ish€ more due to bus ticket savings) for saving 2h on the road each trip.
With AKL it will depend on the individual deal saving, I guess, but even without AKL I will reach FB Silver and maybe Gold with a couple mid/long-haul conferences and the FB AMEX Gold.
I'm aware that short-term I'll pay a premium but mid-to-long term I hope to a) enjoy easier travelling and the choice of more and better flight times/frequencies, b) be flexible with free extra luggage and save the fee on long-haul flights and c) save a few euros by using promo awards and miles.
Also, my old credit card is running out, so I need one with travel insurance anyways and I might as well get the FB AMEX Gold then.