Is the gain on the sale of a home exempt if I was in the military and lived there as my primary residence?

You would be able to exclude the gain based on the information you provided.  In general, to qualify for the exclusion, you must meet both the ownership test and the use test. You're eligible for the exclusion if you have owned and used your home as your main home for a period aggregating at least two years out of the five years prior to its date of sale.  

If you received a 1099-S for the sale, you must report it on your tax return.  In TurboTax, you can enter your information in the Sale of Home in the Wages & Income section.  I highly recommend going through the section and keeping the worksheets TurboTax creates even if you are not required to report because these are invaluable if the IRS would audit you.