Ok so I have heard a lot of conversation over the topic of Flynn and Rapunzel's relationship...now toi either like them ou toi don't I guess is how it goes and I must admit that when I was watching the movie the first time I went "Wow...they fell in l’amour when?!" but the thing is literally if toi blink at an exact moment toi could miss what really pointed it out in the first place. Here's an analysis of their relationship throughout the movie.

1. In The Beginning:

Flynn was a thief...and self-centered and pretty much just a selfish really cute animated character. All he cared about was his cartable, sacoche correct? Ok so when he crawls into the tower...gets hit in the head with a frying pan...multiple times, Rapunzel tells him her dream. Ok so Flynn just finds this girl to be a real annoyance and only agrees after she expresses that he will never find his beloved satchel. Rapunzel is just curious of this new person she's really too naive to realize that she likes him...don't get me wrong though because Rapunzel actually seems very smart and well-read.

2. The Moment:

Ok so there is a scene after the "Snuggly Duckling" number where they are in the tunnel and Rapunzel has just basically distracted a bunch of thugs...something Flynn Rider couldn't do. He compliments her...now remember how selfish Flynn was in the beginning? Hmmm...he's complimenting someone...something very VERY out of character for him. Then she ask him about his backstory and he explains how he simply doesn't talk about it...well I don't remember if it's before ou after she ask him that...but all of a sudden Flynn looks back at her and just...smiles. That's when all of a sudden I went "OHHHHH! He likes her!"...or he's getting there! Rapunzel is intrigued par him...ofcourse his selfishness is Lost on her but still he isn't just her guide anymore...for some reason the two of them have a connection and slowly they are beginning to see this. When the guards montrer up Flynn pushes Rapunzel in front of him and actually lets her run out first...I also thought that was unselfish.

3. Real Name:

So after escaping the guards and the stabbington brothers Flynn and Rapunzel are stuck in a small incavement and it's filling up with water quickly. After many failed attempts at trying to escape Flynn gives up and he tells Rapunzel that it's hopeless. She tells "Flynn" that she's sorry and suddenly he just goes "It's Eugene" and he spills that his name is Eugene Fitzherbert...and tells her his dislike for it. Not much "Romance" blooming whatever toi call it happened in this scene just the fact that Flynn opened up to her...even though they were just about to "die"

4. Doubt:

They sit around the campfire and she shows Flynn her glowing hair to which he "Doesn't freak out" about...he tells her how he grew up in an orphanage and how he read a story about a guy named Flynnegan Rider...she tells him that she actually likes "Eugene Fitzherbert" a lot more...he scoffs but toi can tell that makes him happy par the small smile on his face...Flynn goes off to get firewood while Rapunzel smiles and thinks about what he just told her...then Mother Gothel shows up giving her the satchel...Rapunzel tells her that she thinks he likes her to which her mother will have none of. She tells her that if she returns what he original wanted he will leave her. Flynn comes back after Mother Gothel dissapears and ask Rapunzel what's wrong...to which she a dit she was just caught up in her thoughts.

5. The Kingdom:

When Flynn wakes up he sees Maximus and even though they are enemies Flynn is ready to put up with Maximus if it will make Raunzel happy...another unselfish deed. They go into the kingdom and theres a montage of them lire and buying things and Rapunzel starts a dance in the village square...Flynn smiles at her from the side watching her twirl...when Maximus begins to see that the famous thief Flynn Rider is falling for the girl with the long golden hair...pushing him into the dancing him and Rapunzel reach fro eachother a few times trying to get a dance with eachother and in the end they end up hand in hand...both happy yet embarassed and quickly let go.

6. I See The Light:

Flynn decides to be romantic and take Rapunzel on a bateau to get a good view of the lights...her dream. She expresses to him how she's terrified of what will happen when she sees them and what she will do after...and with a small smile he tells her that she will have to find another dream. The first lantern is sent up and Rapunzel's face lights up and as plus are realeased Flynn watches her face and smiles at her from his siège in the boat. Rapunzel turns to Flynn suddenly and he's holding to lanterns for them to send up, they do. Rapunzel returns his stachel and tells him that she isn't scared anymore and if he knows what that's like...lowering the stachel he smiles and says he's starting to. Looking into eachothers eyes they finally realize something that has been developing over the last two days...they like eachother...not l’amour but like. chant to eachother Flynn grabs her hand and fixes her hair...about to Kiss her he looks at the rive and the stabbington brothers are there.

7. A Trade:

They go tot he rive and Flynn takes his cartable, sacoche with him as he goes off into the woods telling Rapunzel he will be right back. When he reaches the Stabbington brothers he throws the cartable, sacoche at them not even caring about the treasure inside anymore...but then they say they want the girl with the magical hair...and he definalty not giving them that...well long story short he's tied to a bateau and it looks like he's betrayed Rapunzel. Mother Gothel was behind it all.

8. The End:

So how can someone who has known toi for two days willingly give their life for you? Well if that person believes he is nothing plus than a common thief he might look at the girl that has interest him plus than anyone else and go "Hey she has much plus to live for than me" and she's probably thinking "As long as he's happy...I will be too"
So toi know the end he ends up "dying" for Rapunzel...he cuts her hair so that she can be free and happy...but her tear saves him.
They kiss...their first Kiss and return to the kingdom.
When they are on the balcony and she's walking towards her mom he is quietly watching from behind and when the family hug he simply smiles down at her for he knows she is happy...then he is pulled into the hug himself.
The way the story ended was nice...we saw the couple Kiss once more...and toi can tell...that really they are made for eachother. Rapunzel rolls her eyes at his playfulness and Flynn Rider is now a hero plus than a thief.
Oh and toi got to rememeber they didn't get married until years after...so really it took years for them to REALLY fall in love.

So yeah just thought I would right that out...this is all opinion based so don't take it too seriously!