For life, that would be hell on Earth. Doubt that will occur. He'll probably be put in general population and probably join some white supremacist gang to survive. Don't think any inmate would really care about him murdering Kyle and Littlefield. Murder is a badge of honor in most prison populations. Hardcore inmates are not very patriotic.
There are mainly only (2) offenses that all types of prisoners abhor - pedaphiles and snitches.
Don't be too sure about that. There are lots of vets in outlaw motorcycle gangs and, surprisingly enough, many are quite patriotic and conservative in their politics. I think there are a lot in prison would enjoy the chance to take out a coward who shot a brother vet in the back.