Born in 1938 in Málaga, Spain. Brinkmann is son and grandson of Germans.
In 1957 he founded with other painters “Grupo Picasso” in Málaga. In this very same place he presented his first solo exhibition in the “Sociedad Económica de Amigos del País".
In 1961 he moves to Hilden Gabelung in Germany, near Düsseldorf. In Cologne he establishes contact with representatives of the Fluxus group and assists with the first happenings of Vostell. Brinkmann establishes a close friendship with the musician Cornelius Cardew.
In 1963 during a visit to Málaga he meets the actor Anthony Quinn who buys many works for his foundation.
The same year the MoMA in New Yor buys one of Brinkmann's work for its collection.
In 1966 the artist returns to Spain and resides in Málaga. He dedicates himself to painting, drawing and sketching. Participates in the exhibition “Artistas Gráficos Españoles” in the Modern Art Museum of Johannesburg, and represents Spain in the IX and X Biennale in Sao Paulo and also at the I, III, IV, and VI International Drawings Exhibition at Rijeka (Croatia).
In 1977 he also wins the Prize for Paintings at the Festival International de la Peinture, Cagnes-sur-Mer (France). Between 1977 and 1979, he was Senator during the Constituent Legislature process, in group Democratic Senate, from Malaga, Spain.
In 1992 Brinkmann opens another studio in Madrid, working between Málaga and Madrid.
In 2008, he is invited to be a featured artist at the III Beijing International Art Biennale. Since this same year, works regularly in China.