BA customer on American
 

I have 2 flights tomorrow from MSY to DFW to London heathrow. I am ticketed as a BA customer but both flights are operated by American.

I cannot check in online. I get a "This itinerary is not supported for check in at this time. Please check in at the airport with an agent."

BA says don't worry about it and check in online. I do know AA has oversold the flight (I have a seat reserved but there is a warning indicating that the flight is overbooked). Is checking in online going to get me booted?

I can't miss that flight to London. I'd have to wait til the next day which would be a disaster.

Is it unheard of if I went to the airport tonight and checked in, in person?

BA customer on American
 

Don't they provide the AA ref number so you can check I. With AA? UA always gave me a Lufthansa, Swiss, .... Ref if it was needed

It's not clear if you are trying to check in at ba.com or aa.com. If aa.com you need your sabre locator which you can get from BA or
https://www.checkmytrip.com/
https://www.virtuallythere.com/
Also are you within 24 hours of your flights?

BA customer on American
 

You can check-in 24 hours prior to first flight departure. If online check-in fails, in-person airport check-in will always work.

BA customer on American
 

If you goto select seats then select the American seats it will give you the AA booking reference number and you can check in on aa.com.

Thats the biggest problem with codeshares. Especially when one airline locator doesn't exist on the other.. ie BA codeshare on AA metal. Your amadeus booking number won't work on AA. And as a codeshare, you won't have a Sabre number either.

There is a Sabre number. You just have to get it. It is normally on the travel information paperwork near the details for that flight. Otherwise, call BA and ask for it.

If you go into BAEC, you can check in 24 hours prior to your flight. I have done this previously when I flew LHR - LAX - SFO - ORD - LHR on AA metal (BA Flight #) just couple of weeks ago~~

+1
There's indeed a Sabre number and a simple call to BA customer service will get you this number.