Well, I'm assuming you know where to find a Feebas. But if you don't it can be found by fishing directly beneath the bridge near the weather institute during the day and by a rock at the southern end of the same route at night, right across a house. If you fish in these locations at the given time, you will encounter Feebas only and nothing else. Although beneath the bridge be sure to fish to the left or right and not up or down as you won't find a Feebas
To chain fish, here's a guide to it
https://www.youtube.com/watch?v=MSDPldvOXeg