Try and check your bags all the way to CNX at JFK. If you do this you will be able to use the International Business Class lounge on your arrival...assuming your transit time is long enough. When it is time for your domestic departure follow the sign for domestic transfers. Here you will be given a sticker that says "International Baggage" and you will be directed to a special immigration area. Your departure card will stapled into your passport and you can proceed to your domestic gate. Collect your baggage and clear Thai Customs in Chiang Mai. This is assuming you are arriving and departing BKK...If your flight to Chiang Mai is departing DMK--- you must clear all formalities at BKK and change airports.