If it is a through booking of AMS-ORD, BA will sort out the rebooking on the day; just turn up for the new flgiht time and enjoy the EUR600 compensation ( unless it is an extraordinary circumstace)
If it is 2 separate bookings, then once BA has got you to London, it has done its job and you will liekly be up for any change fees/fare differemce for getting the LHR-ORD changed
Getting to airport early will likely just extend your travel day - I would be very surprised if with such a short delay, it would rebook onto KLM
If you really need to be there at 13:30, perhaps cancel and rebook on KLM