What can I do with leftover "Sweet and sticky" marinade?
The main concern with re-using anything that has come into contact with chicken is salmonella, however as you are talking about using marinade that has been cooked you shouldn't have any safety concerns, so you can use it in a different dish. 

As for what to do with it that's hard to say for sure, it depends on how thick it is. If it's really baked on then you're likely to find that all the goodness has been cooked out of it and it will have a burnt taste and not much else. If it's more of a gel and tastes good you could use it for a variety of things, anywhere you'd use barbecue sauce basically, for instance:


Dipping sauce for fries, breads, etc
Substitute pizza sauce
Sauce for burgers