Poe was always touching Finn, he's always been that kind of guy and his new companion is irresistible. It was just friendly things, a hand on his arm to steer him one way or the other, a hand on his chest for emphasis, an arm around his shoulders for familiarity, and hugs simply because Finn deserves all the affection he's missed and more.
It doesn't take long for Finn to mirror the contact and Poe is elated when he does. It's not every day the handsome Stormtrooper who sweeps you off your feet isn't such a Stormtrooper on the inside. Finn is bright, and enthusiastic, and sweet, and quickly wins over everyone he comes in contact with. So yes, it's a crush. Of course it is. It was crush at first sight (and Poe has seen a lot of people).
There is the small matter of Rey however. She's a bonfire, beautiful, powerful, intense, but she's not something you can put your hands on. Not if you're not Finn anyway. She's not prickly or distant, she's just cautious and Poe doesn't blame her. Strangely, and certainly born of something he wasn't there to see, she likes to hold Finn's hand. Not for long periods of time, but they definitely do hold hands where people can see. Mostly when going from place to place. It's like they're afraid they'll loose each other on the way.
Soon he catches Finn touching Rey the way they touch each other. Casual, companionable, more than just hand to hand contact. Rey seems to like it, but Poe will wait for her to initiate in their case. He isn't THAT kind of a guy.
It's not long mercifully. They're certainly together enough to up the odds, the Falcon needs a lot of TLC. Soon she's leaning into him to see things, squeezing past him in narrow spaces, manhandling him when she's tired of verbally instructing him. They butt heads a lot, strong personalities are bound to, but it's never mean. One glorious time he offered an idea she found particularly inspired and she swiftly grabbed his temples to kiss his forehead. Another gesture she's shared with Finn albeit a little more gently. He still lets her do most of the touching, but from then on the dam is broken.
One night they were all squeezed onto Finn's bed resting backs to the wall talking about whatever; Poe with his arms thrown over their shoulders. At some point Rey had turned inward to wrap an arm around his waist. More outright cuddling than he'd ever done with Finn.
"I am the luckiest man in the system." He voiced, squeezing them just a little to get the point across.
"What?" Finn asked turning towards him, Poe willed himself not to think about how close his mouth was. He had hoped his statement was just taken as is, and not really questioned. He was taking too long to answer apparently and Rey was looking at him now too. He wasn't really prepared to lay it all out under such scrutiny.
"You know?" He offered. They looked at him, Finn with open curiosity and Rey with all the deep intensity Finn wasn't using on top of her own. "You guys are my friends, and here we are and it's nice." Nobody is shooting at us, we're not running for our lives. Nothing is on fire that's not supposed to be." He bluffed convincingly enough for Finn, but Rey did her best to burn a hole through him. "Would'ja cut that out?" He broke out in goosebumps. Was she going to use the force? Could she read his mind? He didn't feel that tell tale suffocating sort of feeling you get when someone else is inside your brain, so probably not.
Instead she did something much different. She straightened herself out from her comfortable slouch pressed against his chest, and she kissed him. It wasn't messy and passionate, but it was no gentle innocent peck either. He made a little noise in surprise and that got Finn's attention.
"Hey!" he slipped out from under Poe's arm, "Not fair!" They stopped kissing and pulled away from each other. "I want one?" He mumbled turning away from the pair. Poe laughed and pulled him back in. He just grinned at the other man for longer than Finn wanted to wait. He's the one who brought their mouths together. Finn clearly had no idea what he was doing, but he followed Poe's directions well.
There was a huff from Poe's other side and Rey climbed into his lap to separate them.
"But-" is all Poe really got out before her hand was over his mouth and she was the one kissing Finn. He let them have at it for a little bit, because if he were being honest it was pretty great to watch, before he licked a stripe along Rey's palm.
"Eugh!" She pulled away from Finn and yanked her hand from Poe's mouth. The latter laughed as the young woman searched for something to dry her hand on...Finn. Who squawked and tried to wipe it back onto her. Rey tried to scoot away but Poe wrapped his arms around her and held her fast.
"Oh no you're stuck here now!" She wiggled in his grip. Beside them, Finn just laughed. He realized his mistake when she got free and pounced on him pinning him to the bed tickling him until he wheezed. Rey took her full weight off him as he tried to catch his breath. Hardly a second later Poe was wedging himself between them and the wall and trying to get an arm over them both.
"I see you're trying to kill me." Finn was trapped under Rey and held partially in place by Poe.
"Us? Never!" Rey assured him as she climbed off him. She kissed his cheek and curled into his other side. Finn lifted an arm so she could rest on his shoulder.
"Well maybe only smother you with love" Poe shrugged.
"Love?" Finn turned to beam at him.
"Yeah kid, love."
"Love!" He turned his head towards Rey who mirrored his smile. "Love?" He pointed back and forth between himself and Rey.
"Love." She answered.
"Love?" he points over his shoulder to Poe.
"Yes Finn, I love him too."
"Good, good. Yeah good." He rolled over to face her, kissed her forehead, and combed his fingers through her hair. "Poe?"
"Yep. I love Rey." He provided an answer as he spooned himself up against Finn. He pressed a loud kiss to the back of his neck then spoke up again. "I hate to ruin this moment here, but if we're gonna stay like this the pillow is at the other end of the bed."