Are bleeding kit syringes single use?
You can likely use it multiple times.

Obviously, you don't want to mix different fluids in that are incompatible; you could clean the syringe by drawing in and out a bunch of times, but its probably less convenient than just keeping a separate syringe for different fluids. 

They may fail at some point (likely the gasket), but that's probably fine; just use a new syringe when it fails. This may occur between multiple uses if you don't clean/if the materials degrade the syringe over time. But its not a big deal.

Note that even humans  have fairly high success rates reusing syringes, particularly drug addicts in first world countries and oral syringes for babies (which is closer to the type of syringe your bleed kit has). Though, obviously, for medical reasons, you don't always want to (usually don't) want to reuse a syringe.