"a gene only spreads when it's good for its self"

I assume you mean that it is being good for it's own copies, the gene itself could end up in the belly of a predator but any of the group beyond immediate kin could benefit. You could call it selfish as it is only looking after its type, it would survive because as long as it is in the population other "guardian angel" copies of the same gene will be there to ensure its survival.

As kin selection works, I assume the same mechanisms work across the entire group, not just down the generations.

It's interesting that a gene that say, makes an animal more likely to vocalise when there is danger gets fixed in the population. The effect is not good for the individual or its copy of the gene, but good for the entire group's survival relative to the external population.