Is installing a headphone jack in the Elekit 22 doable?
Would some resistors need to be put in just before the headphone output?
Three weeks nobody answers you? cant figure that out as there are plenty here who have a lot to say on adding resistors to the output of an amp to make it "doable" as you say for headphones. Can it be done with the stated output of 12 W/channel certainly. Maybe somebody will come charging in to your rescue and I wont have to say any more.
I would think that modding an expensive piece of kit like that would be best left to the manufacturer . You'd probably only invalidate the warranty, and where would you put the jack anyway, without spoiling the look of the package?
Buy a passive switchbox to switch the source and a headphone amplifier. It'll look even more impressive if you buy the right things.