What is the value of a 1965 Kennedy half dollar with no mint mark and the letters F A G on it?

Mint marks were suspended from 1965 to 1967 due to the changeover from silver to clad coins, so it's perfectly normal for all 1965 halves to be "plain", with no mint mark. The letters most likely were added by someone using a metal punch, which makes the coin a damaged item with no collector value. In any case, it's only 40% silver so its melt value is roughly 1/7 of the price of an ounce of silver. With silver in the $15 range as of this writing (mid-2016) that's roughly $2.