According to a post on rgp by the WSOP tournament director (
http://tinyurl.com/2glmo), players can find out on May 19 whether they will play on day 1 (May 22) or day 2 (May 23). I'm not sure why you're worried about what time the final table ends on Friday. It depends of course on how fast the table plays. If you are going solely to see your brother play, maybe you could just schedule a flight out of Vegas for Thursday the 27th, because if your brother does happen to make the final table, I'm sure he wouldn't mind paying the change fee on your flight.
But if you're interested in watching the final table to completion (regardless of whether your brother is there), schedule your flight for Saturday May 29.
Full schedule is here:
http://www.pokerprofessor.com/Wsop2004.aspx