SuperMan as the flawed hero? Thats......not good.
Ok so in story telling there are a set of archetypes that appear in classical story's through all of human history. I do not know that everyone one would agree on exact number of them or how to define them but there is one archetype that is always popular. Superman is the Demi-god.
Specifically the direct offshoot of the Hero archetype. Characters like Hector, King Aurthur, and The Kid from Bastion are good examples of this. Characters that are at once larger then life but still very human and vulnerable. The hero is always virtuous and stalwart. The hero knows what the score is and which side they are on, honest to a fault and always ready for whatever challenge is over the next horizon.
While the Flawed Hero is someone who want's to do good but is largely obstructed by their own flaws and constantly screw up. Characters like Spiderman, Batman, Ironman, Lancelot, and Achilles.
The Demi-God could be any other type of hero (Hero,Anti-hero,Flawed hero) accept that their traits are always magnified. Hercules is a good example of a flawed Hero who is also a Demi-god. Always seeking to great deeds and slaying monsters but never able to be happy for long because his own rage are a strong as his valor and he kills friends and foes alike.
But Superman is the Hero Demi-god. He is everything the hero is but with the power to act without compromise. He is the ideal and perfect exemplar of his archetype. He fits into the same category as Jesus, Buddha, and Maui.
Of course good characters are often a mix of more then one archetype just like real people are. This is why the flawed hero is generally more interesting then the strict hero. They have issues that we can relate to. But it is just not who Superman is. I do not know if you could make that work for him unless he goes through character growth and becomes the Hero he wants to be by the end of the movie.