Klinger was born in Dornbach near Vienna. In 1895, he found his first employment with the Vienna fashion magazine Wiener Mode. Here he made acquaintance with Koloman Moser, who later would be his teacher; Moser recommended him to the Meggendorfer Blätter.
1896 saw him moving to Munich where he worked as an illustrator for the Meggendorfer Blätter and others. From 1897 to 1902 he was a collaborator to the eponymous Jugendstil magazine Die Jugend.
In 1897 he relocated to Berlin, where he worked extensively as a commercial graphic artist until 1915. Together with the printing house Hollerbaum und Schmidt, he developed a new fashion of functional poster design that soon gained him international reputation. In 1912 he designed the poster for the Rund um Berlin air show in Johannisthal. In Berlin he also contributed to Das kleine Witzblatt, Lustige Blätter and Das Narrenschiff humorous magazines.
Beginning in 1918, Klinger designed a comprehensive and noted campaign promoting the "Tabu" company's cigarette rolling paper, that was advertised all over Vienna in 1918/19. Klinger devised a promotional strategy, spanning from small-sized newspaper advertisements to billboards and painted firewalls - construction site fences and winterized fountain paneling were used as advertising space, too.
Being of Jewish descent, he suffered from national socialist harassment. According to Viennese police records, he was registered as moved to Minsk on June 2, 1942, i.e. deported. Presumably, he was killed the same year.
Probably towards the end of 1937 he designed his last poster for the Ankerbrot-Werke factory. The Jewish-owned company was transferred to "Aryan" proprietors in 1938; after 1945 legitimate ownership was restored.