He graduated from Tartu High School of Sciences, then studied in the Commerce Department of the Riga Polytechnical School in 1904–1910 and eventually graduated with a first-degree diploma in Germany.

Kukk headed the financial department of the Estonian Provincial Assembly in 1917–1918, served as Financial and State Property Minister of the Estonian Provisional Government in 1918–1919, was Minister of Finance of the Republic of Estonia in 1919–1920, and then Minister of Commerce and Industry in 1920–1921.

[2] He resigned as Speaker upon being appointed State Elder, an office he held until 2 August 1923.

After Kukk left the Riigikogu, he was succeeded by Johann Kana.

After the Soviet Union occupied Estonia and the other Baltic states in 1940, Kukk was arrested by the NKVD and deported to Russia.