Entei can be found in the Dark Cave in the Johto region only after defeating the Elite 4. You need to find Eusine and he will give you a quest to get coal by defeating monsters in the Dark Cave and lighting the torches.

If you accidentally defeat Entei, he will respawn in 7 days. Once you capture Entei, he will no longer respawn.

You can also receive an Entei Egg as an Ultra Rare drop from defeating the Legendary Dogs Boss on Four Island.

1) Fly to Blackthorn City.

2) Go south down Route 45 and take the bridge to the west to reach the Dark Cave.
3) Follow the line on the map to the left to reach Eusine.