As the comment above notes, the SI brochure states:
In both English and in French, when the name of a derived unit is
formed from the names of individual units by multiplication, then
either a space or a hyphen is used to separate the names of the
In Section 7.80, "Hyphens and readability," the Chicago Manual of Style advises (emphasis mine):
A hyphen can make for easier reading by showing structure and,
often, pronunciation. Words that might otherwise be misread, such as
re-creation or co-op, should be hyphenated. Hyphens can also
On pg. 14, the AIP Style Guide echoes the advice of the Chicago Manual:
Modifiers made up of two or more words are usually hyphenated. When
such hyphens forestall ambiguity, they are essential.
The salient quantity in kilogram meter per second is the kilogram-meter; after all, what's being measured is not the meter per second (velocity) or the kilogram per second (my weight gain on weekends), but the kilogram-meter per second.
So to highlight the composite term formed by multiplication, I (and this source) would write:
The kilogram-meter per second (kg · m/s or kg · m · s -1 ) is the
standard unit of momentum. Reduced to base units in the International
System of Units (SI), a kilogram-meter per second is the equivalent of
a newton-second (N · s), which is the SI unit of impulse.