I would recommend to stay with intimate Casa de la Memória, popular with tourists but only absolute top artists perform here. Two performances each night, at 7.30 and 9. Buy tickets one day in advance or try to reserve at flamencomemoria@gmail.com (they didn't use to accept reservations and sold tickets only one day in advance). Note that they have changed location to Calle Cuna 6, right in the centre of town.

World class artists such as Pastora Galván, Adela Campallo, and Rafael Campallo have performed here about once a week for the past couple of years. Pastora Galván was voted best female flamenco dancer 2010 by Spanish critics. The program for your date is not set yet, but it will be published here in short: http://casadelamemoria.es/

Maybe you're lucky! But as said, only top notch artists(singers, guitarists and dancers) here.

A clip of Pastora Galván (now on tour in New York, Washington, Tampa, Miami and London): http://www.youtube.com/watch?v=k2SBUcrJgeQ

Later in the night (after midnight) there are several great flamenco/sevillanas bars/clubs in Triana - a true cradle of flamenco culture - just across the city river Guadalquivir.
El Rejoneo and Casa Anselma are fun and Mantoncillo is as genuine as it gets, here anything can happen:

Casa Anselma: http://www.youtube.com/watch?v=Gw1atBQq_u0
El Rejoneo: http://www.youtube.com/watch?v=bPZT3ADgWsw
Mantoncillo: http://www.youtube.com/watch?v=qtkqvASPgIY

Thanks kimhe. I'll try emailing them and will definitely go out to Triana and bar hop a bit.

Any suggestions about the transport to Algamitas?

Would be plenty of taxis in Osuna, nothing to worry about at all.