1 BTU (thermochemical) = 1054 J
and
1 J = N m = 10^3 N mm
1 BTU = 1054 J = 1054 x 10^3 N mm = 1.504 x 10^6 N mm
Therefore,
1 mm/BTU = 1mm/1.504 x 10^6 N mm = 9.4 x 10^-7 N^-1 = 9.4 x 10^-7 kg^-1 m^-1 s^2
That still doesn't make sense.
You have a measurement of length, energy and mass. The formula makes no sense what-so-ever.
if you invert it and use a = 9.8m/s2
(1BTU / mm) x (1054J / 1 BTU) x (1Nm / 1J) x (1kgm/s2 / 1N) x (1 / 9.8m/s2) x (1000mm / 1m) = 1x10^5 kg