Based on information at this website Covers by JH. Could the song be
"Tax Free" by Carlson and Hansson ? "They licensed the track Tax Free to Jimi Hendrix".
I couldn't find a version with the intro you mention, but it seems a pretty good match to the other facts.
The track is on one of the compilations released after Hendrix's death, "War Heroes": 1972, also on a later compilation South Saturn Delta: 1997.
Hendrix live 1969, Denver
Hendrix live 1969 Copenhagen
Carlson and Hansson original
More information on Carlsson and Hansson from wikipedia
The band was active in the last few years of the 1960s and played
instrumental jazz fusion, largely based on improvisation and are
considered one of the pioneers of progressive rock. Hansson and
Carlsson played a few times with Jimi Hendrix in Stockholm, and
Hendrix recorded the Hansson & Karlsson piece "Tax Free". After a few
years the duo split, Hansson continued his musical career whereas
Carlsson focused on his acting career.
Hansson died in 2010. Carlsson died in August 2017.