Although the exact issue in which the relationship truly began is open to debate, as different readers have different interpretations, the flirtation certainly started in X-Men #3 and was (interestingly) instigated by Rogue. The scene opened with Rogue diving off a board on Magneto's orbiting mutant sanctuary, Avalon, while they were held prisoners by Lehnsherr:
GAMBIT: Not too shabby, chere. Finest-kind, Olympic class cannonball.
ROGUE: You like, Gambit?
GAMBIT: I like. That an' more.
ROGUE: Better watch it. Ah touch your bare hand with mine. Ah'll absorb your powers and psyche an' all your mem'ries.
GAMBIT: Maybe. Maybe not. Wan' take the risk, li'l river rat?
ROGUE: I... I... No!
The tension continued in X-Men #4 with the infamous basketball game between Gambit and Jubilee, Wolverine and Rogue. After Rogue supposedly used her powers to stop a ball, the game degenerated into a mutant-rules free-for-all.
After she slammed a ball into his chest with all her considerable strength, Gambit charged a ball, knocking Rogue through a window. He helped her up and draped her over his arm in best romance novel style, which led to the following scene:
GAMBIT: A prize worth
the winning! You may have lost the game, you and your furry partner, but, for you, at least there is
a chance to claim something from the day! Champagne, candlelight. Magic time, chere.
CYCLOPS: Er... Gambit... maybe you should curb that romantic soul of yours.
JUBILEE: Yeah, the lady's not interested, big G.
GAMBIT: No? Ah, Jubilee, how little you... .
ROGUE: NO! Keep your slimy paws off'a me, Gambit! You know Ah can't make flesh-to-flesh contact with you without drainin' all your powers anyway!
GAMBIT: Perhaps. But don' nobody know how Gambit loves a challenge.
Despite Rogue's protestations, she eventually agreed to a date. As Gambit anticipated that she would blow him off, he was shocked when she appeared dressed to the proverbial nines, although she explained it thus:
GAMBIT: Hello. Now what's this? Chere, for me?
ROGUE: You wish. A lady has to look her best when she goes out on the town, Gambit. After all, there might be some real gentlement at that restaurant.
Wolverine and Jubilee decided to tag along 'to make sure the boy treated Rogue right', while Beast provided transport, but the date never got off the ground as the five were captured by the infamous Strucker twins - Fenris.
Their second date - happening four issues later in X-Men #8 - was a picnic, which also ended in disaster, although it seemed to begin well enough:
GAMBIT: So, it's not the champagne and candlelight dinner I imagined when I asked you out, I suppose it'll have to do in a pinch.
ROGUE: I thought you'd appreciate me makin' you an' ol' fashion Cajun meal with muh own two hands.
GAMBIT: If I made a list of things to do "with your own two hands", stirrin' gumbo wouldn't be on it.
ROGUE: Ya certainly know how ta get under a girl's skin.
GAMBIT: I'm trying.
ROGUE: Gambit, please! Ya know even the slightest physical contacts means Ah'd absorb ya mind and powers!
GAMBIT: Worse fates spring t'mind, chere.
ROGUE: That's all Ah'd need - thoughts o' you runnin' through muh head twenty-four hours a day.
GAMBIT: How'd dat be any different than now?
She, then, runs away from him, although it is clear that she wants to be caught. If she had really wanted to flee, she would have flown, rather than ran which allowed him to chase her. However, both of them were disappointed as, between Bishop attempting to kill Gambit, leading to the infamous boisenberry pie incident, and Belladonna, Gambit's ex-wife appearing to tell him of a threat to the Guilds, the situation degenerated rapidly with the team leaving to battle the Brood in New Orleans.
Although Belladonna's sudden arrival did shock Rogue and she was initially very frosty towards Gambit, his ex-wife and her got on surprisingly well to the extent that they discussed certain birthmarks that Remy had in certain interesting places. Her curiosity was obviously piqued as she was the one to make the next move in X-Men #12, much to Gambit's surprise!
GAMBIT: Nice view.
ROGUE: Was that a statement or a question?
GAMBIT: Take your pick. Ah, old habits. No flirting here. I was meaning t'have a word wit' ya, neh? 'Bout what's been goin' on an' all - me talkin' about m'wife, Belladonna; you tellin' me how ya really feel 'bout that Longshot boy.
ROGUE: Listen, cajun... Remy, Ah don't know what Ah'm feelin', shugah. Ah don't know what's going t'happen between us. Just gonna wait an' see what way the wind blows.
Although the phrasing is not overtly flirtatious, save for the 'was that a statement or a question?' line, it was accompanied by her teasingly removing his bandanna and tossing it into the wind. (Come on, symbolically undressing him?)
It took tragedy to ultimately cement the relationship. In X-Men #15, Rogue was blinded by Strobe when battling the MPF, and was forced to rely on Gambit to provide a pair of eyes. In X-Men #17, then, he took the opportunity to teach her a lesson about trusting and not trusting him by almost having her walk off the end of a diving board, leading Xavier to comment:
XAVIER: You play a dangerous game, Gambit, but that seems your speciality, doesn't it? Of all my X-Men, you are the most unknown to me. You want Rogue's love but you don't want to fall in love with her, do you? You want her to declare herself yours, but you will not commit to her. Why? A dangerous game for her, but even more so, I fear for you.
Where and when did the 'dangerous game' begin to become reality? Where and when did Remy fall in love with Rogue?