There is not a veteran discount. But you should see if you qualify to use Free File.
If you qualify to use it, there is another full-featured free version of the software:
Try Free File:
You qualify if your income was $36,000 or less, or $69,000 or less if active duty military, or if you qualify for Earned Income Credit
If you switch to Free File you must create a new account and new user ID.