This can only be done on heroic or legendary as far as I know.

When Cortana mentions "My Mother's Shadow", take a right, then you should see a vent that has been blasted open.

Enter, then take a left to the end of it, then there should be a dead ODST that has dropped a flame thrower.

It has full ammo, and it will come in handy. There is also a rack of energy swords if you take a left first, but you can still get the flame thrower.