I think there are very few Google hits because we've got two idioms butted against each other. Neither is exactly common, but they're still in use.
The first idiom is "get in line," which is often used metaphorically to mean conform to societal rules, as in this passage from Eric Bogosian's Wake Up and Smell the Coffee:
I'm not fighting the system, I'm part of the system. I toe the line. And I do it for a very good reason: I'm a sheep. I am a gutless sheep.
So, when they say, "Get in line," I get in line, you know? It isn't like I want to get in line. I hate getting in line. "I'm a rebel, man! I used to smoke pot!"
.. but in the long run, I have to get in line .. that's the deal. Because if I don't, then maybe nobody will, and if nobody gets in line, then what do you have? Chaos!
The other idiom is "soldier style," which can refer to many things, from fashion to landscaping to a rough style of living, or even to any kind of behavior considered typical of among fighting men:
She is never seen without the cumbersome leather purse she wears soldier style on a long strap crossing her breast.1
Stand pavers on end (known as soldier style) to create a deep border for paving projects.2
Drew and I rose with the sound of the bugle on the following morning. We had promised each other that we would begin our new life in true soldier style, and so we reluctantly hurried to the wash-house, where we shaved in cold water...3
Individuals started the march with rations for five days and in typical soldier style lightened their load by eating them in three. Thus hunger and the failure of the supply wagons to keep up, coupled with exposure to rain and wind, weakened them further.4
But in the context of your excerpt, I think it means, as you surmised, dutifully following orders. In other words: act like a soldier. Get in line, get in line quick, and follow your marching orders – no talking back.
F O O T N O T E S
1Dennis McFarland, The Music Room, 2001
2Tom Lemmer, The Complete Guide to Masonry & Stonework, 2006
3James Norman Hall, High Adventure: A Narrative of Air Fighting in France, 1918
4James R. Arnold, Shiloh 1862: The Death Of Innocence, 1998