If you get to the CAN airport, you can take the Guangzhou subway/metro & get off right outside China Hotel.

Take Airport South station (Line 3) to connect to Line 2 & get off Line 2 at Yuexiu Park station - follow signs to Exit #D1 - brings you out on the sidewalk just outside China Hotel side entrance.

Also taxi or bus from CAN airport to China Hotel - subway/metro is piece of cake.

Not sure about flights with Delta miles? - Dragon Air from HKG to CAN is quick/reasonable price, but they are OneWorld (American Airlines) I think