If you add an augmentation with +kick damage to an armor piece that does not already have kick damage, the kick damage from the aug will not show when inspecting the armor piece. If, however, the armor piece does have some kick damage and an aug with kick damage, it will show the total properly. Either way, it will add to the total in the Stats tab appropriately. This is just a display error on the item inspection. Note: I'm not sure if this occurs with augmentations that provide other skill damage mods (e.g. Frenzy), but it might be worth checking those as well. The Relife Adornment (129892) for WAR, RNG, BRD, BST is what is used in the example below.
What you describe also happens with Frenzy: mods added to items without a Frenzy Value will not display a Frenzy value but it will be reflected on stats page. mods added to items which do have a frenzy value will correctly show the sum total of item & the mod inserted.