Your choice of kilner jars indicates you expect your gift to be displayed, at least for a while. So you need enough room for over 6 pounds of honey product.
If so, I think pint or quart jars. You could easily use 4 quarts, depending on shape, because I assume you will not wish to crush the product.
5 kilos of honey will nearly fit 1 gallon. We used gallon containers for 12 lbs.
This should make a sweetly attractive gift. Or, several gifts.