When they discover they've got a crush:
There's a bit of a process Dutch goes through before properly selecting a partner, which includes a rather harsh evaluation (he liked all types of people, but he did have to sort out who was most likely to defer to him and who would prove to be too annoyingly headstrong). It's not easy to tell when Dutch is actually sweet on you because his tone always seems naturally flirtatious, and he looks at you like you and he are the only people in the world.
How they confess/hint:
His hints are subtle to those who don't know him, but otherwise, it appears rather obvious if he's finding himself falling for you. He gets very touchy, brushing against you, touching your shoulders, and can go as far as him kissing your hands in greeting/farewells. If he comes to the point of actually confessing, he comes up with some akin to a poem, weaving into it all the details about why he's found his heart beating for you, and how he could no longer contain his affections.
How to win their heart:
If there's one thing that Dutch stresses is important to him, it's loyalty. He needs to know you're in his corner, on his side, and believing in his ideas. He doesn't mind some dissent, not finding interest in a mindless drone, but he's more likely to fall for you if you're a like-minded individual. He'd really enjoy having intelligent conversations with you, feeling like you were just as smart as he was and had the same refined tastes.
How to break their heart:
Betray him after him admitting his love for you, whether that's turning him in, selling him out, or cheating with another person. It'll be the only time anyone sees Dutch struggle to kill a person (if turned in/sold out), because they have a code by God does he love you. He loved you so much, and this is how you treat him? After all he's done for you to make you happy and keep you taken care of? He laments over the failed relationship because the two of you seemed so perfect for each other, but don't think that'll stop him from doing what needs to be done.
Things that make their heart flutter:
Dutch doesn't often have the time to spend with you romantically, he's got a lot on his plate, so someone who actually takes the time to ask him about his day and have him vent his problems to them wins his heart quickly. He'd also fall for a person who gives a good massage, or helps him manage his stress/responsibilities around camp.
Their type:
Dutch really does like people who seem upper-class (meaning they look rich, but don't necessarily have to be rich). He likes someone who's well-read, a little strong-willed but who won't constantly start a fight with him over his plans. He would want someone adventurous, willing to upturn their own life to travel around with him, and who was hardy enough to deal with the various difficult situations thrown your way.
Goals in a relationship:
Dutch knows it's a romantic ideal, but he does enjoy the thought of having something akin to a soulmate in life. He filters through those he's interested in in hopes of finding the right person, the one who clicks with him best, and helps him achieve all that he's dreamed of. Going farther than this, he's not quite sure what he wants, feeling as though he's raised enough kids for a lifetime even if they aren't related by blood, but if life happens to have him settle down somewhere, perhaps he'd give the idea a chance.