Probably a rotating Satellite or space junk.
The description twice as bright as any star,is that as bright as Sirius
the brightest star in the sky which wouldn't have been too far from said flashes.?
If a Satellite is very high say about 5-10000kms it will still receive the suns light even though the sun is way below the horizon.
I have seen many what I call flashers,if you have a pair of binoculars you can actually see some minor flashes before the big ones.
That they cant be seen again is because they have gone into the earths shadow.
Cheers