...the December [gamma ray] flare was brighter than the full moon...
This is common language in physics; for example, the intensity of a particle beam coursing through a particle accelerator is referred to as the 'brightness' of the beam. No doubt, in the present context, the meaning is something like this: the gamma ray intensity of the flare as measured by a gamma ray telescope was greater than the light intensity of the full moon as measured by a light-gathering telescope.
How shall we get there when [our?] own solar system is 100,000 light-years across...
Our Milky Way galaxy is about 100,000 light years across; our solar system is only about 7.336 billion miles across (about 0.0012 of a light year).