Hi,
Make sure that DL have actually reissued the tickets for AA flights. In case, if they haven't reissued the tickets, you might have to run to DL counter and get the tickets reissued as INVOL reissuance. If the e tickets have been reissued, you could check in at the kiosk without any issue. If not, you might have to run around. Go to :
http://www.aa.com
and use the AA record locator and confirm that your reservation is all correct and an e ticket number has been generated.
Thanks and Regards
taran_2005