Flynn and Rapunzel work so well together because of how they find ways to appreciate the little things about each other. The way I see it is that they both look at the other one and admire strengths and traits that they themselves wish to possess.
Rapunzel sees Flynn as someone who has seen so much of the world. She loves that Flynn has the confidence and bravery to be on his own. While Flynn is witty and charming, as Mother Gothel was, he showed Rapunzel that jokes don't have to be made at her expense. Rapunzel looks at Flynn as someone who is actually protecting her. She spent eighteen years in a tower with someone who took her for granted and only wanted her for self-serving reasons. Flynn doesn't want to own Rapunzel, he just wants to love her and show her everything she's been missing. He constantly encourages her to be brave and seek adventure, just as he has loved doing for his entire life.
Flynn allows Rapunzel to be herself and he cherishes every second of watching her live life to the fullest. He's inspired by her zest for life and love of everything that surrounds her. She doesn't look at grass or butterflies like everyone else does, and he adores that about her. It makes him take another look around and not take everything for granted.
I think it's obvious that Flynn didn't have the confidence to be himself most of his life, but after meeting Rapunzel and seeing how she so bravely owns who she is without shame, he has a new desire to not be ashamed of any part of himself. Flynn loves looking at Rapunzel as she meets new people and talks about her passions with them. It makes him take an interest in others that he'd never really had before. Rapunzel has inspired Flynn to be less selfish and more giving. He never had anyone to care about and love until she came along. Every single day that he gets to be a part of her new life, he's so wonderfully grateful.
Flynn grew up an orphan. He had to become an adult and learn to take care of himself so quickly. Meanwhile, Rapunzel was stifled from growing up and exploring the possibilities of life. Flynn allows himself to feel more childlike around Rapunzel because she brings it out in him. With Flynn's help, Rapunzel is confident enough to experience everything the world has to offer. Flynn is happy to encourage her to be herself and chase new dreams.
They'll always defend each other. They'll always choose each other. They'll always build each other up. More than anything, they'll always be there to remind each other that they are worthy of being truly and deeply loved.