The biggest flea market in Barcelona is Fira de Bellcaire, but everybody knows it as Els Encants (in Catalan) or Los Encantes (in Spanish). It is held every Mon, Wed, Fri and Sat in Plaza Glories. You can reach it by Metro, Glories or Encants stops.
From the Barcelona Municipality Website: http://w3.bcn.es/ab/asia/equipament/controller/0,2317,70381_70816_3,00.html?accio=fitxa_eq&idEquip=92086009468