Depends on the material...
your Khaki probably has tritium phosphor, as do most Omegas made since 1960 or so. Tritium is a radioactive isotope of hydrogen, with a half life a little over 12 years. This would lead one to expect that the dial should lose half its luminosity over 12 years, but there is more to it than that. The phosphor itself loses strength over time, and there is no telling how long the tritium sat before going into the luminous compound, or how long the compound sat before being painted onto the dial, or how long the dial sat before being installed in the watch, or how long the watch sat around before you bought it...Phew! My Speedmaster Automatic had a noticable glow in broad daylight when I got it; 2.5 years later, I would say it's about 1/8th as bright.
On the other hand, the newest Omega watches are now shipping with a luminous compound called Luminova. This is a non-radioactive product which is charged by ambient light and releases that light over time. It is much better at this, though, than previous compounds, and a couple of hours in light will last all night long. The upshot of this is that you get a bright dial that stays bright. You can tell if an Omega dial has the new compound as it will be marked just SWISS MADE rather than T SWISS MADE T on the bottom.