I would say - no - not without cleaning (and drying) the syringe in between medications...preferably sterilizing it. You run the risk of, among other things, changing the medications when you mix them (which will happen automatically if the syringe has not been cleaned).
I don't know about these specific meds - but be sure that you can even give them to the bird at the same time without impacting their viability.
As Waynette says - if a sterile needle (or even empty syringe) is required - the answer absolutely is "no".