Although you could fly to BKK on KE or NW and the take a Bangkok Airways flight to Phnom Pehn, the KE flights arrive in BKK late in the day which would require overnighting in Bangkok.

Why not just take KE from the USA to Phnom Pehn?? You would get reliable service on well maintained aircraft and Delta MQM's and base miles. I haven't checked, but you might even fly KE metal on a Delta ticket, via the codeshare. Why not call Delta or KE and book the trip? I suspect that taking the entire trip on one carrier is less expensive than transiting via Bangkok and buying a ticket on Asia's Boutique Airline, Bangkok Airways

KE 689 flies from ICN to PNH daily, departing Seoul at 7 PM and arriving at 10:55. You could easily connect to this flight from JFL by taking KE 82. You'd leave NYC at 12:40 and arrive ICN at 5:10 the next afternoon. Go to the KE lounge after arriving ICN, take a shower, check your email and grab a snack and head out to the gate for the flight to Cambodia, about a 5 hour flight.