Fleurquin was born in Montevideo and started his career at Defensor Sporting in his native Uruguay. His good performances were rewarded with a call up to the Uruguay national team for the 1999 Copa America, and this lead to Austrians Sturm Graz bringing him to Europe. He enjoyed 2 years with the Austrians and was again included in the Uruguay Copa America squad, this time in 2001. His performances this time lead to him being signed by Galatasary where he played in the Champions League. After only a year in Turkey he moved to French club Rennes, and after only 13 games Córdoba bought him to Spain. He started well but picked up an injury after less than half a season, and his struggle to win back his starting place opened the door for Cadiz to sign him. This season he has battled Manolo Perez for a starting spot, and his impressive performances and experience means he currently has the edge over the Spaniard.