Burns went to Cardinal Newman High School in Bellshill before enrolling with the Royal Scottish Academy of Music and Drama in Glasgow, taking up a Bachelor of Education degree in teaching music. He did not finish the degree, completing only 3 years of the course. He broke his finger, which is why he did not go back, though he has also said that he was not at ease with the teaching part of the course.[2]
Burns joined Mogwai just before the recording of their second album, Come on Die Young. He had already played a few gigs with the band beforehand as a flautist and occasional pianist. According to Stuart Braithwaite, Burns joined the band because he was a "good laugh".[3] Burns is a versatile multi-instrumentalist and contributes (among other things) keyboards, guitar, vocals (mainly through a Vocoder), and flute. He is also the only member of Mogwai with a formal foundation in music theory, but he claims he is "a bit rusty".