Looks like OP may have booked these on separate tickets as WS does not appear to sell JFK-ICN through fares. Note that DL Amex first bag free policy only applies to DL marketed and operated flights and thus would not apply here. Not sure about Medallion checked luggage benefits. Also through checking may be complicated assuming ticket was not issued by DL. Note that through check policy mentions having DL ticket in order to through check partner operated flights -- https://pro.delta.com/content/agency...e-policy-.html