In all probability, none of the below is true, and it comes into the story simply because Roger Price had a typical laymans knowledge of physics and took one scientific fact without understanding the context in which it existed (which also seems to have happened with regards to biology in Hitler's Last Secret.
The idea in question is time dilation. It's a generally accepted scientific principle that the faster that one travels relative to another person, the less time that will pass for you. This is not just a theory, it has been
demonstrated using high spped aircraft and atomic clocks.
In simple English, if you are standing next to a high performance aircraft and I take off in it and fly around at Mach 1 for a couple of hours and then land next to you, less time has passed for me than has passed for you. The higher the speed I travel at the less time that has passed for me. This is not a matter of perception to me - the amount of time that has passed from me is every bit as real as the time that has passed for you.
The time dilation effect is insignificant at low speeds (and in this context even the fastest speeds attained by anything we have developed are extremely low). But if someone could travel at a significant proportion of the speed of light, then the effect becomes quite noticeable - effects like the one described for Kenny above.
So far so good. The problem arises when we consider how did Kenny travel such vast distances? My perception of teleportation is that you drop out of normal space for a short period into hyperspace and you are then able to drop back into normal space at the location you want to be. The problem is that such a method of travel should not create a time dilation effect - the time spent in hyperspace is too insignificant and the time in normal space does seem to be equal to the time spent in hyperspace. A jaunt takes fractions of a second - in terms of normal space, this is obvious. It can be seen that the time taken for the jaunt is very small because we have heard TP communicating telepathically prior to a jaunt and then appearing very rapidly. And we know that only brief periods are normally spent in hyperspace from conversations between the TP.
So it seems that time in hyperspace and time in normal space pass at the same rate. If that were not true then on those ocasions when TP have spent longer periods in hyperspace (Slaves of Jedikiah, The Medusa Strain, and The Blue and the Green) upon their return there would have been a noticeable time lag - for effects such as the non aging of Kenny we would need to see lags of days when mere minutes had elapsed.
So we can't put Kenny's non-aging down to a difference in the normal elapsation of time as occurs in hyperspace.
We also can't put it down to the normal time dilation effect because that would require high speed travel in either hyperspace or normal space and teleportation does not seem to involve any actual physical movement between two points - merely departure from one and reappearance at the second point, with the teleporting being never actually existing between the two points during the course of the jaunt. This is contradicted by information in One Law where it seems that they travel down some sort of beam, but that is problematic as if that occurred we would expect to see a very large time dilation (as the Trig is 800 light years from Earth, even if a long distance teleportation took one minute (which seems to me to be accurate based on One Law) speeds approaching 420 million times the speed of light would be needed to be achieved in order to allow such transportation to occur. The time dilation at such massive speeds would be very significant - there would be a significant amount of travel backwards in time which could not possibly be because Stephen would have then arrived before TIM had even brought up the amount of interference between the Trig and Earth and certainly couldn't have been transmitted until after he had already arrived (I love relativity but it certainly gives me a headache - not to mention the fact that it requires tenses that don't exist in normal English grammar!)
In terms of travel to another galaxy (Spyra in Kenny's case) then we are dealing with speeds that render the 420,000,000 C described above absolutely tiny.
In essence if time dilation does occur by whatever means Kenny has of travelling, Kenny should be travelling backwards in time in the perception of the others on the Trig. If the method does not involve time dilation, Kenny should be aging normally.