Well it depends if kg/day was a typically quoted unit. For example, if I was trying to express how fuel efficiency decreases as car speed increases, I might say that in a 100 km journey, you need 5 litres more fuel for every km/h you drive over 80 km/h. So the number would be 5 l/km/h. Which I would hope would be interpreted as 5 litres per (kilometre per hour). Now, strictly speaking, that's just plain wrong, but, like the aforementioned "convention" that spaces, divide signs, and so on are often not used in the strict BODMAS fashion, people would probably gather what I mean from that statement 9 times out of 10.
I certainly wouldn't write it as 5 l.h/km (5 litre-hours per kilometre). I would most unambiguously write it as 5 l.km-1.h, though again, that's not very helpful either.