If they will eat the meat straight away, go for it! They're only kittens so should eat often and as much as they like
If they don't want to eat the meat at first, mix it with the wet food and then slowly reduce the amount of wet food - over a few days until they eat just meat.
The fact that only one kitten is unwell indicates to me that that kitten is more sensitive to the adverse effects dry/low quality cat food has on any cat. Just like humans, some are more sensitive than others. That doesn't mean that the dry food is fine to give to the cat that doesn't show any symptoms though!
For example, I have a sensitive stomach. If I eat a McDonalds meal I will be stuck in the bathroom for the next few hours. Not pleasant. My sister has a normal stomach and has no problems with McDonalds. Does this mean that McDonalds is healthy for her and bad for me? Of course not. It's equally bad for both of us; I just react to it easier than her.
I am assuming that there's no medical issue with either kitten - which is why I said to take them to the vet to get them checked. Especially considering it's been going on for a week now.
If I were you I'd want to see the vet first, then start the meat diet. Of course, this is up to you to decide. You could also just start the meat diet and see how that goes - again it's up to you and if the kitten does have a medical condition you risk it dying before you can get it to a vet. If it doesn't have a medical condition and just reacts to the food, it may well be fine after a day or two on the new meat diet. It's up to you to decide.