For simplification purposes, let's assume that the rope is hanging straigt down from the kite, with the kite having just enough uplift to stay at a constant height.
In reality, the kite would be stretching out from the vessel at an angle to actually pull it into a certain direction, similar to modern container ships using kites:
For these container ships, of course, the kite's altitude does not matter too much - a couple hundred meters above the surface winds are already fast enough.
For now, let's calculate the best-case scenario: The kite is not actually excerting any forces on the ship. This can be taken into account at a later point in time - you will see why.
Thanks to the data sheet provided by @AlexP we know the minimum breaking load to weight ratio for different thicknesses of hemp rope - a material which was broadly available in the Victorian era.
We can calculate the maximum length of a hanging rope using the equation:
is the maximum length of the rope
is the mass of one meter of rope
is the minimum breaking load
If we solve for :
According to this equation, we want to have the best - to - - ratio possible.
If we look at the data, the best ratio is found in the thinnest ropes with thicker ropes becoming slightly, but progressively worse.
So, let's solve the equation for the thinnest rope in the dataset (6mm):
Allthough this might sound like a lot, we are talking about the best case possible!
So let's make some more assumptions.
Now it gets fuzzy.
Your question states that the kite should be used to save fuel, not as a single source of all propulsion necessary. So effectively every little bit more of force the kite excerts apart from the one used to keep the rope upright will help reduce fuel costs. Additionally, we don't know the weight or drag coefficients of the ship - making it impossible to assign any numbers.
For example, we could say that we want the kite to be able to excert at least the same force as the static thrust of an engine of a modern cessna single-engine aircraft (~500 lbs / ~2000N).
Let's compare the value of 2000N used for propulsion with the forces excerted by the rope at maximum length. Even if the rope has the minimum thickness of 6mm we still have to deal with 2850N of sheer gravitational pull. If we choose a more useful thickness like 34mm the weight of the rope alone will attribute for 84000N alone. In this case, the generated thrust becomes neglible enough to not take it into account.
Of course, no airship engineer would design his kite ropes without safety margins. Let's assume a conservative 50% of the maximum allowed force. Because the calculation above scales linearly with its components, we can assume that the rope would have a maxmium length of about 5000m.
Wether 5000m is enough height or not is up to you to decide. I would say that it isn't - especially because you can have the airship just accend to the preferred height and let it be carried by the wind, requiring the engines only for course corrections or additional speed.