Kolkata is written in the key of F Phrygian.
According to the Theorytab database, it is the 6th most popular key among Phrygian keys and the 55th most popular among all keys. The F Phrygian scale is similar to the F Minor scale except that its 2nd note (G♭) is a half step lower. Chord progressions in Phrygian often rely on the major chord built off of this 2nd scale degree (G♭ major) which gives the key its distinctive sound.
See the F Phrygian Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!