Two years.
And also, that's complete bullshit. Arlong will not get NEARLY as strong as Luffy over these two years, or his growth curve becomes higher than the main character's, which just doesn't work in a shonen manga.
The only thing that he could have done to quickly gain strength in order to challenge Luffy after both the gears and haki, would be to eat a completely amazing Devil Fruit, and even if fishmen can do that, would they even want to? Not being able to swim… even if you can breathe underwater still, and walk on the ocean floor.... That sounds awful.
No, if Arlong makes an appearance in front of Luffy on fishman island, it will be a cameo so Luffy can show off just how awesome he is by using Haoushoku Haki to 1HKO arlong without touching him.
But I don't think Arlong will show up at all, and your theory of him being able to challenge luffy at all is just completely psycho.
My theory was based on the fact they would be underwater. On land Arlong wouldn't at all be stronger then luffy but underwater where luffy's gears and normal attacks would be alot slower it would give arlong an incredible advantage.
Plus I'm not expecting luffy running around throwing his King haki all over the place. It would defeat the purpose of rayleigh saying its not something you can train like the other haki's.
And for arlong it was three years. Luffy defeated arlong before sailing on the grand line. Assuming arlong was able to escape capture from that weak mouse marine like hatchi then he could have been training or went to the grand line on his own. If people expect buggy to become a shichibukai in 2 years of training why not arlong make another pirate crew/army and take over fishman island. Jimbei is no longer a shichibukai so the WG and the humans have no reason to try and bond with Fishmen.
This would be perfect for the straw hats to come in, defeat whatever threat is happening on fishman island. While defeating the threat, they show the fish people that humans adore them and want to be friends. When they leave, the straw hat pirates claim fish island is under their protection and the future pirate king.