A few days ago I bought Aeroflot flights to Ho Chi Minh City (return). Yesterday I bought Vietnam Air flights from Ho Chi Minh City to Siem Reap (one way, just after arrival on Aeroflot). Would it be possible to combine both flights, so that we can check in directly to Siem Reap, given that both airlines are in the same alliance? If so, how do I sort it out?
Can you combine them, no, they are separate bookings with separate carriers.
Can you check your bags through? Perhaps. As they are separate tickets, you do not have the right to check them through, but the agent checking you in, wherever you are starting, may do it for you since they both alliance members.
Can you check in (ie get your boarding passes all the way to REP)? Probably not.