Except the OP flew AA codeshare on BA, thus AA is the carrier on the last segment, and solely responsible for the baggage. BA would have been responsible if it had been a BA flight (last carrier is responsible for lost baggage), but by booking the AA codeshare, it becomes an AA flight and it is entirely an AA responsibility. Unfortunately AA has no office at AMS, making dealing with them difficult. Servisair followed the correct procedure if it had been a BA flight, but not correct for AA codeshare (no doubt BA's systems rejected the form when it hit BA).

So, very important to immediately call AA and initiate the lost baggage process. BA may or may not have forwarded it to AA. This is one of the side effects of booking codeshares, and something to keep in mind in the future. When arriving at airports without a presence by the codeshared airline, it can be a major hassle. Personally I would have made sure to book the BA code instead of AA precisely because of this factor.

As for compensation while waiting for lost bags, the norm is after 24 hours you get a set amount based on the class of your ticket. On BA is is approx. USD 50 for Y, USD 250 for J and USD 500 for F; you must have receipts for clothes, etc. to match these amounts. If the bag is found, you get this money. If the bag is never found, this amount is deducted from the compensation limit for your bag. I don't know what AA's limits are, but they will be similar.