At the age of twenty-five he migrated to New York, where his sisters lived. There he began cleaning flats and working as a dishwasher. He studied a degree in Humanities at the College of Staten Island, where he also completed a doctorate. His thesis studied the Galician poet Eduardo Pondal, from whom he reconstructed and published his epic poem Os Eoas. In this same institution he became Professor of Spanish and Head of the Department of Romance Languages.
During his time in New York, Rincón established relations with Galician exiles, such as Emilio González López, and took an active part in the Casa Galicia, of which he was president in 1986-1988 and 1991-1992.
He returned to Galicia in 1992. In 1993 he received the Medalla Castelao, and in 1996 he was elected mayor of Redondela, where he passed away in 2019 (Sources: “Adiós al exalcalde Amado Ricón”; Marcos Santos, “Amado Ricón bo e xeneroso”, Memorias de Casa de Galicia).