What percentage of the universe's energy is rotational kinetic energy? Obviously there is constant exchange between different forms of energy, so presumably only an average could be estimated, assuming it is not an ill-posed question.
Also, even if a fairly precise figure could be given, is this likely to be any use, for example in relation to other cosmic parameters?
 A: First off: distinguishing between rotational kinetic energy and linear kinetic energy is not an intrinsic distinction; the name alludes to pattern of motion.

As we know: the solar system is is a gravitationally bound system; the celestial bodies of the solar system are all orbiting the common center of mass.
So from that point of view: all of the motion of all of the objects of the solar system can already be categorized as bound system motion, which means that the associated energy can be categorized as rotational kinetic energy.
The combined mass of our Galaxy is a gravitationally bound system, so in that sense all of the motion component at galactic level is bound system motion.
At higher levels of organization it starts getting ambiguous.
Many galaxies are destined to merge in the future. Our galaxy and the Andromeda galaxy will merge in the future. In general the Universe is expanding, a proces that tends to increase distance between galaxies. Groups of galaxies with sufficient gravitational interaction to have a merger in their future (despite the Universe expanding on them), can be regarded as bound to each other.
I think that is about as much as can be said about structures in the Universe being organized in bound systems.

Our Galaxy and the Andromeda galaxy
When our Galaxy and the Andromeda galaxy merge the energy of the motion of moving towards each other has to go somewhere. The distances between the stars of each galaxy is so large that initially the galaxies will just pass through each other. But once that has happened the total population does not separate again. The two galaxies will disrupt each other, ending up as a single merged galaxy. It seems to me the merged galaxy will have more rotational kinetic energy than the rotational energies that went into the merger. What was added was the energy of the motion of the two galaxies towards each other.
The probability of two stars actually colliding is low, but if a such a collision occurs then kinetic energy is converted to heat.
Galaxies contain clouds of gas. Those clouds do collide, of course, and the kinetic energy of their relative velocity will convert to heat.
