Falckenberg studied philosophy, literature, and art history, initially in Berlin and from 1896 onward in Munich, though he did not complete his studies. He wrote several plays and devised productions for theater groups. Between 1903 and 1913 he worked as a freelance writer and wrote plays, some of which were performed with considerable success at various theaters. He was made the Munich Kammerspiele's head dramaturge in the 1914/15 season and then its director and creative director three years later. In this capacity, he and his ensemble moved into the Schauspielhaus in the fall of 1926 and remained there as director for the city from 1939 until the building burned down in 1944.
Falckenberg created a scenic, post-naturalistic theatrical style and staged plays by such figures as Strindberg and Shakespeare, which laid the groundwork for future traditions. He discovered and trained young actors like Therese Giehse, O.E. Hasse, or Carl Wery. Briefly imprisoned mid-March 1933, he was allowed to remain at the Kammerspiele with minimal freedom, albeit with a limited selection of plays, even though he was not a member of the Nazi Party. He received the Goethe Medal for Art and Science and was included in Hitler's list of the divinely gifted as one of the four most important theater actors in 1944.
After the end of the war, he was no longer allowed to direct, so he withdrew to the countryside and gave private acting lessons in Starnberg. The drama school affiliated with Munich's municipal theater was given Falckenberg's name at a commemorative ceremony on March 1, 1948, and bears his name to this day.