Defense (DoD) budget is $900 billion now. When you also account for veterans' health, expenditures on nukes (goes to the DoEnergy), military stuff in space (goes to NASA), border protection, etc., the total national security spending tops $1.5 trillion. That's not counting the interest on past wars.
Medicare + SS is about $2.6 trillion. With Medicaid, it's up to $3.3 trillion, but this still gets you nowhere close to "all military is 1/6 of ss and medicare".
Even if we are more conservative about how we count "all military" - for instance, include veteran's health and nukes, but not CBP - it still doesn't get us close to the 1/6 number.
Would you explain your reasoning and numbers a bit more?