Looks I was mixing up the IATA rule with the US rule. The IATA rule does go as I stated. The same airline policy throughout, but each checkin gets the allowance from that policy.

The US rule goes by the marketing carrier of first segment or of the MSC. The carrier that checks you in determines which. Thus KLM can go by either DL policy for intra Europe flights or DL policy for EU-US. KLM forum is really where this needs to be asked. Most airlines go by the first flight. In which case only one is free. They might waive the 2nd bag fee since flying onwards to US. However only one bag is free at each subsequent checkin. If they go by MSC, then that's DL policy for EU-US and get 2 free.