I think a week or 2 is usually recommended, but it depends on how sensitive your cat's digestive system is. I chop and change wet foods all the time and it causes no problems with my 2. I change dry a bit more gradually, but a few days is usually sufficient. I'd start by adding a tiny amount of the new food to the old and observe if there are any problems. If not, add a bit more the next day.
I just gave Gizmo the better food in a heap since she would pick the stuff she did not like out of her bowl if it was mixed and dump it on the floor. She overturned her bowl with the Newman's Own, ignored Felidae and Serengeti and all but three other premium brands. California Natural, Royal Canin and Nature's Logic were smash hits without any 'break-in periods'.
As one of the others said, it really depends on the cat. I've changed Bijou and Mika over to several different foods recently and usually a couple days of mixing them is all it takes. Fortunately neither seems to have a sensitive tummy and no litter issues so we've been lucky that way.
Doing the change gradually certainly can't hurt anyway.
I changed straight over the to new dry food with no problems. They were eating 2 different dry foods as it is (Lily liked the adult food rather than the kitten food, and Stumpy liked the kitten food rather than the adult food), so I got Science Diet kitten food, and both love it.
No digestive problems, but I knew neither cat was terribly picky, and neither had shown any signs of digestive problems before that, so I figured they'd be fine.
funny. in trying to figure out what Wick liked best, we gave her like 8 different foods in the course of a week, with no problems. Now, we switch off the fish one and the chicken one every day to keep things interesting. Still no problems. But I'll keep this in mind if I get this kitten.
Here is what I have found out... Kittens under 6 months 7-14 days , young adult(over 6 months ) to early senior 7-8 yrs 7-10 days , "olsters" 14-30 days .. It depend s on the extent of change: ie are you going from lots of by products and corn to little to no corn and no by products( would take longer) , If your truly moving flavors ie chn and rice to a true beef and rice( any time major(meats ) proteins are switched go slower ... same food different flavor ( not being in the first five ingrediants ) 4-7 day s is sufficiant for many