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Family name Fleiri (Fleire , Fleiri ) , around the world, is a rare surname. The surname Fleiri is habitual in Latin America and the Caribbean, particularly Venezuela, where it is a rare surname, Argentina, and Colombia, where it is a very rare surname. Not in comparison with a country's population, the name is most common in Latin America and the Caribbean, particularly Argentina, Venezuela, and Brazil. Much less frequently, Fleiri is the forename as well as the last name.