Hi, did you assign the OnClick() events? This must be done for each button in each scene.
For example: Level1 -> Canvas1 -> LevelWinScreen 1 -> UIBackdrop -> NextLevelButton -> Button script -> OnClick() should be set to: LevelLoadButton.LoadLevelByName with "Level2" as paramer value in the field below the function name.
If that's not it, you could watch this video again to see where you might have missed a step:
https://www.coursera.org/learn/game-design-and-development-1/lecture/wxIlO/game-...
Good luck,
Acido