Officially the Military has to accommodate your needs when they don’t impact the mission. If you plan ahead and notify the people at BCT of your needs, they should be able to accommodate you. It might not be easy, but it should be kosher. I would contact whatever base your BCT is at immediately so they can prepare for your needs. There are a number of Orthodox Army Chaplains, I don’t know any of their contact info or where thay are (I’m an Air Force Chaplain). You should contact the Jewish Welfare Board. They give ‘hashgacha’ to Jewish Chaplains and lay leaders. They will be able to tell you who/where the Army Chaplains are and will also be able to help you get accommodation.
http://www.jcca.org/JWB/ Also try the Aleph Institute http://www.aleph-institute.org/ they also do a lot of support for Jews in the military.
Are you from Milwaukee? I am. I moved away after high school and I miss it there. If you’re part of the west side community there are a few people there who know me.
Good luck, and remember that there are always people out there to help you, don’t be afraid to ask for it.
gmar chasima tova