[1] He played for KS Flamurtari Vlorë from 1975 to 1981 as a left back and managed the club.
As a player, he started every game at left back in his six-year tenure at Flamurtari Vlorë and also appeared 7 times for the Albania National Football Team.
At the age of 19 he became a football player with the newly formed KiF Shkëndija in Tirana.
In 1977, at the age of 26, Leonidha signed with Flamurtari Vlorë, where he would play alongside Edmond Liçaj, Kreshnik Çipi, Petro Ruçi and Vasil Ruci as well as his brother Spiro Çuri for two years.
In 47 years of Flamurtari Vlore football, they finished 11 times in the top five without Leonidha.
Two years after retiring from football, in 1983 Leonidha became manager of KS Flamurtari.
[5] In the 1985–1986 season for Flamurtari they finished 2nd in the Superliga tied with Dinamo Tirana with 38 points losing only to goal difference.
Leonidha Çuri's formation was dominant even though he couldn't score a goal in Barcelona.
Partizan were leading 2–0 until the 76th minute when Sokol Kushta scored an absolute beauty to take Flamurtari into the next round.
In the same season Leonidha Çuri won Flamurtari its second Albanian Cup after beating Partizani Tiranë 1–0.