OK, i had a similar prob a few years ago with my landlady.
I hate being around when people are traipsing through the house and my landlady decided to sell the house I was renting. I spoke to her and told her that although it was her house, I was paying her £350 a month to live there and that it was hardly fair to
a) bring people around if she would not be responsible for my property while I wasn't there
b) bring people around every night - after all I was paying to live, not feel like a stranger in my own home.
I suggested two nights a week - I think it was Tuesday/Wed, when she was able to give the Estate Agents a timeslot to come around - think it was after 5.30 and before 8.00. The Estate agent could arrange 6 half hour viewings through that time and usually it was just 2 or 3, and finished by around 7. She did ring once or twice and ask if it was ok to bring someone on another night because they couldn't make Tues or Wed and I agreed, as they were one-offs.
It's not ideal, but it's a compromise that might work and you can always take your mate down the pub for a pint while they are there if you'd prefer. TBH i'd probably be a bit hacked off if I was him, paying out moving costs etc just to find you've got to put up with people coming round all the time and having to move again immediately!
You need to sit down and find a compromise that suits all three of you. Either that or hide your flatmate in the airing cupboard
edited to say: ... and if you don't want to move, make friends with next door and get them to play loud music when the prospective buyers view. <joke>