The IVs for Entei are locked in the first time you encounter Entei in the wild, and likewise for Raikou (but locking one of them in doesn't lock in anything about the other). You can save after freeing them from the tower, but then you pretty much have to hope that the first time you encounter one of them, it appears shiny, otherwise it'll never appear shiny in any future encounters unless you reset and go back to that earlier save where you haven't encountered them yet.
If you have another copy of the game available to trade with, you can trade them over just for the purpose of unlocking their Pokedex entries, so you can at least track their movement around the map to get that first encounter in a more reasonable amount of time, and keep restarting through all the times they appear but aren't shiny.
