They "made up" for marketing purposes. Shaq lies about a lot of that sh** like the media didn't know that they were really tight. No, they hated each other, and Kobe drove Shaq out of town by giving the team a me or him ultimatum. Given that Shaq was older and overweight and Kobe was prime and marketable, it wasn't a hard decision. As it is, someone got to them and told them that being petty was bad for business, so they publicly made up in Shaq's second year with the Heat. And then they weren't anything. Shaq went to Kobe's last game, again for marketing purposes. Then he never saw him again.
Maybe the animosity dissipated with time; but they were not good buddies really ever. Closest I can think is Shaq praising Kobe for a couple big games in the playoffs where he himself had been contained and someone had to step up.