The main issue isn't whether this is a good idea, it's whether you can find a designer who would be interested. I have a business finding app developers for entrepreneurs and small businesses, so I can tell you from experience that most designers and developers don't want equity or a percentage of profits; they want cash. And that's understandable. They have an extremely valuable skill, and they'd rather have cash than a slice of equity that might be valuable or might be worth nothing. There are so many risks in involved with apps that most pro designers or developers wouldn't take that kind of risk. In this case the deal is even worse since it's a percentage instead of equity.
This kind of value disconnect with entrepreneurs is common. The problem is that you see your app as an exciting, sure thing. And that's only right; as a startup owner you should be excited and motivated about your big idea. But for a designer, it's not their big idea, it's their job. And so they want to be paid like with any other job. The only time I tend to see this kind of arrangement is when the entrepreneur has a friend that they're going to work with. Even then though you see equity more than profit percentages. I'm not saying that finding a designer who's willing to accept a percentage can't happen, I'm just saying it's not that likely unless you have a history of startup success and an impressive resume.
This may not be what you want to hear, but it's the situation that you have to deal with. So what do you do? There are a few things. First, keep your app plans as simple as possible with very few features. That means a simpler and cheaper design. Also, consider whether you actually need a pro designer. It's not necessarily a given that you do. Obviously you need some sort of design for your app, but depending on how complex it is you may not need a separate designer, you may be able to just do some mockups of your own. In fact, if you're planning on making revisions to your app post-launch, you'll end up having to revise the design anyway to accommodate the changes. Of course, if you're a commercial business that needs an app as a sales tool, then you might need a designer to make sure that your design has some polish to it. Overall, I'd say the key thing for most apps is picking the developer, not the designer. Of course, I can't give firm advice since I have no idea what the app is or what you're trying to do.
I consult on app planning and developer hiring, so feel free to reach out if you'd like some more individualized advice.