I fly BOS-AMS and AMS-BOS once a year with a (just shy of) 7kg, 15lb dog.

Delta at Boston has no issues with size, they never question it. Boston Logan requires dogs be in their carrier at all times (including the SkyClub) unless it is a service dog. Dogs are not allowed in BusinessEilte; per the Delta no dogs in BusinessElite international (dog) policy.

KLM handles Delta at AMS (for AMS-BOS); KLM policy is 6kg for in-cabin; but they also seem to have some lee-way. At check-in, they ask me how much he weights, and I say 6kg. In AMS, he's able to stay out of his carrier (and visit all areas of Schiphol including the KLM lounge) until just before boarding the flight.

So, basically, I do not believe you will have any problems.

All my other knowledge is with regard to EU doggie passports, and regulations, which would not be applicable in your situation.

My biggest issue is no BusinessElite, or bulkhead seats (which is obvious, because of under-seat rules). I believe the "NO BusinessElite policy" is in keeping with the integrity of the International BusinessElite cabin; but of course, babies and service dogs are allowed (so this is really a silly rule, IMO).

FWIW, KLM also does not allow dogs in Business Class, but Air France does.