Chain fishing is very common to get shinies! I will provide a step by step instruction.
First of all understand that: Chain fishing increases your chance of finding a shiny pokémon. A chain occurs when you encounter a wild pokémon every consecutive time you use the fishing rod while standing in the same spot. get a bite from a wild pokémon Each consecutive time you get a bite from a wild pokémon while fishing at the same spot, your chance of encountering a shiny pokémon increases.
A fish chain occurs when you encounter a wild pokémon many times in a row while using the fishing rod at the same spot. It does not need to be the same pokémon each time. You can run away or KO or capture the wild pokémon without breaking the chain. If you get the message "nothing seems to be biting" when you use your fishing rod, the chain has been broken.
Second:To improve your chances of chain fishing success, put a pokémon that has the Suction Cups ability or the Sticky Hold ability in the first slot of your party. This increases your chance of getting a bite from a wild pokémon while fishing
Third: The guy who gives you the Super Rod in Mélancolie Path will give you a hint about chain fishing if you beat his record of 7 consecutive fishing encounters. He says that you should fish in places surrounded by rocks, or in a corner. The more enclosed a fishing area is, the more likely you are to encounter many consecutive pokémon while fishing. A good example of such a location is in the area south of the Muraille Coast beach, which is part of Ambrette Town. There are some rocks at the south end of the path that surround a patch of water on three sides. You can fish in that patch of water by surfing there and using your fishing rod.
Tips: Changing weather conditions may break the chain. I had a chain of 50 that ended with the "nothing seems to be biting" message after it started raining.
If you have a pokémon that knows Synchronize, you can use it to increase the odds that the shiny pokémon that you encounter has the same Nature as the Synchronize pokémon. However, you have to put the Synchronize pokémon in the first spot of the party, which means you can't use a Suction Cups or Sticky Hold pokémon in the first slot to increase your chance of finding consecutive wild pokémon while fishing.
Chain fishing is not a guarantee of finding a shiny, but your odds of finding a shiny will become much higher than usual.
Also: Make sure you have patience! I like to use a counter on my phone to see how many encounters I have for each fish.
I hope this helped!