I have found some skill upgrades (energy regen, something acrobatics, health upgrade and some more, can't remember names), but I can't find them anywhere. Clicking on any empty slots of a chip (I have only starter 'scavenger' one) does not show any new upgrades. I have two upgrades that are showing and working for the Flash skill (energy and range upgrades), but I can't find any of the one I've aquired by activating skill upgrade beacons. Am I doing something wrong?

Not entirely sure but I think which skill upgrades you can use/slot in also depends on the skill chip itself. As far as I know you're able to acquire better, more capable skill chips in this regard as the story progresses and you get access to other regions of Peh.