Next to the food and sense of safety, I think Allen fell for Link because he indiscriminately roasts anyone with his sass, mainly the people who get on Allen's nerves the most while staying deadpan. Allen can't deny playing exasperated, so for him Link is Goals™ and when he's the one getting sassed he really can't be mad at Link at all and he's so in love with The Sass that he wants more. It's like a metaphorical "please step on me".
A metaphorical ‘please step on me’, oh my god.
Link’s sass is pretty damn amazing, so ain’t no one going to blame Allen for falling in love with that, hahaha. I imagine that Kanda in particular often falls victim to it, which is definitely going to endear Link to Allen even more.
Imagine Allen and Link bonding over private roasting parties where they roast literally everyone in the Order just for the fun of it. Link has most of the cleverest lines, of course, but Allen usually makes Link blush once he’s comfortable enough around him to use his dirty mouth/mind. (Which is very unfair, Allen.)
(Also imagine Allen and Link bantering playfully over a meal, most of their focus on each other and both smiling like the lovestruck idiots they are.)