is s kg^-1 a si unit or does it have to be written as kg s^-1 ?

Answer 1

s kg⁻¹ is not the same thing as kg s⁻¹. The first one is "seconds per kilogram" whereas the second is "kilograms per second." The second one makes more sense (for instance, as denoting a rate of fuel consumption, whereas I don't know of any quantity measured in seconds per kilogram), but be careful that you are not confusing it with km s⁻¹ (I've already seen one person make that mistake on Y!A). km s⁻¹ = km/s = kiloMETERS per second, and is a unit of velocity, and completely different than kg/s.

Answer 2

absorption-emission constant is in s kg-1 i think. I put a link to where i found it below. Constants can be a bit funny with units sometimes.
The other response above is correct, that s/kg is completely different from kg/s, so can't be substituted, even if it seems to make more sense.

Whether your units of s kg-1 is correct or not will depend on where you've found it, but it's not an impossible unit.

Answer 3

doesn't make sense