Boris Gammer was born in 1949 in the Soviet Union — the year is confirmed by the Freedman Jewish Sound Archive at the University of Pennsylvania, though no source gives an exact date or birth city that could be independently corroborated. He emigrated to Israel as part of the same wave of Soviet-trained musicians that brought saxophonist and pianist Vyacheslav "Slava" Ganelin, Roman Kunsman and Nahum Perferkovich to the country in the early 1970s; Hebrew Wikipedia's article on Israeli jazz lists all four together as musicians of that émigré generation, though no source documents a direct personal collaboration between Gammer and the other three individually.

In Israel he became a saxophone teacher in the jazz faculty of the Jerusalem Academy of Music and Dance (JAMD) — independently confirmed through a biography of one of his students, saxophonist and flautist Rachel Mazor, who names him as her teacher there. He also founded and led the Jerusalem Jazz Band, a "Dixie-Freilach" ensemble — one of very few groups anywhere fusing Dixieland jazz with klezmer — formed explicitly, per a contemporary review, to carry on his father's musical legacy after his own emigration from the USSR. The band appeared on Dutch television in 1992 and released the album Songs My Father Played on the Netherlands label Ffortissimo Productions, with Gammer as leader, arranger and clarinetist.

His own leader album, Eight Till Late, came out in 1991 on Jazzis Records as part of the label's "Jazz in Israel" series — eleven original compositions (all but a few credited to Gammer himself) recorded with guitarist Avi Rothbard, pianist Art Bloch, and a rotating bass chair split between Eddie Rezonov and Yaakov Seagull. He remained a fixture of the Jerusalem jazz scene into the 2000s: a 2006 festival review of Jazz-Globus — the international festival in Jerusalem directed by Ganelin — describes Gammer as "one of the main engines" of the event, leading jam sessions there with two of his own saxophone students, Oleg Neumann and Yakir Sasson (the latter now an active bandleader in his own right), and separately performing in a "Retro-Jazz" group alongside the well-known Moscow saxophonist Alexei Zubov. In February 2013 he led his own sextet at a JAMD-affiliated Jerusalem Cinematheque concert built around a Cole Porter program, with vocalist Julia Feldman as guest. His last independently dated activity found in this research is a 2017 saxophone credit on a Lithuanian tribute album, reuniting him with his old Jerusalem Jazz Band bassist Eduard Rezonov. Whether he is still living or active today could not be confirmed.

Gammer worked two related but distinct idioms across his career: straight-ahead, hard-bop-inflected tenor saxophone jazz on Eight Till Late, and the "Dixie-Freilach" hybrid of the Jerusalem Jazz Band, which set Dixieland horn writing directly against klezmer melody and rhythm as a way of honoring his father's music after leaving the USSR. Both strands share a teacherly, ensemble-first sensibility — his standing role at the Jerusalem Academy of Music and Dance and his habit of building bands around his own students (Neumann, Sasson) at festival jam sessions suggest a musician as invested in passing the music on as in performing it himself.