How much kinetic energy is there in the observable universe at any given time? I know that it fluctuates, but, what would be a good estimate for how much kinetic energy is in the universe right now? I know that things cancel it out, but, how much is there?
 A: First of all, I see the Tag is general relativity. I only have a very basic understanding of the subject. So take that into consideration with regard to my comments below.
I agree with Ben Crowell and TechDroid. It's interesting, however, that you are asking specifically about kinetic energy, as opposed to total energy (the subject of the link provided by Ben). I don't see how one can quantify the total amount of energy, kinetic or otherwise. But here are some preliminary considerations, albeit from a classical physics perspective.
Before we can even think about quantifying the amount of kinetic energy in the universe, we would first have to agree on what forms of energy in the universe are kinetic energy. Is dark energy kinetic? Is electromagnetic energy kinetic? Is mass energy kinetic or potential energy before it is released. I see many different opinions on what forms of energy should be considered kinetic. And I don't profess to have those answers.
Then we would need to differentiate between macroscopic kinetic energy (rotational and translational kinetic energy of extended bodies) versus microscopic kinetic energy (internal energy of mass, typically associated with temperature). 
In the case of macroscopic kinetic energy, the amount would depend on the frame of reference in which it is measured. I'm sitting in a train moving along a straight track at constant velocity. I have an earth globe on a desk. I spin it. In my reference frame it has rotational kinetic energy only. In the reference frame of someone on the tracks watching the globe go by through the train window, it has rotational and translational kinetic energy. You get the idea. So there really isn't any single value of macroscopic kinetic energy in the universe just as there is no absolute frame of reference.
In the case of microscopic kinetic energy, I suppose we could estimate the total mass of the universe, its heat capacity, and average temperature, and come up with an estimate. Ah, but then again, is dark energy kinetic? Without an answer to that, our calculation could be considerably off!
All just food for thought.
Hope this helps.
