Download? No. You can extract them through an SGA reader provided you have a copy of the game, or from the flash if you have something like Trillix. You might also be able to find a compilation on youtube as well. But as for individual sounds, there's no download.
It'd be really cool to hear the Guardsman or Kasrkin squad on a soundboard. I never get tired of hearing them shout their lines, whether it's "To arms!", "Hustle up! One, two! One, two!", "Let's see them try to fight ALL of us!" or "It's every soldier for himself!"
But the best has still got to be the Kasrkin's "For the Imperium of MAN!!!"