No, you only get to use the benefits of the power for the single turn it is activated.
Like furious charge, squad advance, and bolter assault; once activated you immediately take the action allowed then the benefit ends. If the power specified, "For X number of turns," then it would remain in effect until X turns go by.
In the case of the above mentioned powers and Into the Fires of Battle, the duration of the power is specified as, "immediately," meaning it occurs once then expires.
A short caveat on out of initiative powers like the ones listed above: a character can only ever benefit from an out of initiative action as a result of a power ONCE every turn. For instance one brother can activate Into the Fires of Battle and another can then activate Furious Charge, but any character using Into the Fires of Battle could not benefit from Furious Charge as they've already made an out of initiative action.