Thanks for sharing this with us.
It's a nice idea, albeit not the first of its kind, a nice idea nonetheless.
I'll base this answer on information I have gathered by searching similar topics online, and speaking to developers.
The idea of developing "for free" has somewhat radically changed over the last decades. At the turn of the 21st century, web developers (the ones who were not already getting paid for it) started getting away from all those free gigs and 'waiting for that great opportunity' type of charity work. I say for free, and you're saying for equity, thus in your mind it might not be the same thing at all... but it is. Why? Because there's no supporting evidence that you will ever be able to pay that developer, nor that the project would become a commercial success. If you came to me offering equity in exchange for this app, I'd think you're just getting away with not paying me for my work, and that's how most will feel. Furthermore, in order to offer equity, you'd have to have some sort of structure in place. An LLC at the very least. This is money you need to inject in the project, although not substantial (that said, it could be for a teenager), it's still part of the budgeting, money you could spend actually paying a developer for her/his work.
I am in no way trying to discourage you, quite the opposite in fact. Here's what I think your options could be:
Learn how to program it yourself – Had you asked the same question on Quora (if you don't know what it is, look it up), you'd have received that advice aplenty. Why should you learn and develop it? Because you will want to have at least some understanding of what the developer is doing. Developing an app is not just scraping some blocks of code that you tie together to make things work and voila. If you have customers, you need a database to keep their records. You'll need to make sure that you can protect those records. People will trust you with their information, and it's your job to keep them safe. The code needs to be secure as well. You'll want to avoid any potential breaches that could lead to breaking things or accessing said records. How can you know any of this if you don't have some understanding of programming, especially when you're relying on someone you're not paying for the current most important task?
Get another teenager onboard – You want to play the entrepreneur card, go for it. I get it, it's exciting, everyone seems to be doing it, and at your age particularly, you're full of ideas and dreams. You should thrive on that and try to make the most of it, I'm serious. This is one idea but you might want to explore others as well (you don't have to go through with them, just lay them down on paper). This said, if that's the path you want to take, you're gonna need a CTO. A Chief Technical Officer in this case could be considered as your co-founder. This model is the most frequent, it seems. One needs to focus on business development (that would be you, right?), and the other, more technical, on the development front. Why do I suggest a teenager? Because I think that's the only way you'll get away with not paying somebody for their work. Reality is that people have bills to pay, lives to lead, sometimes go by, and can't afford such a project "for free". A teenager, however, can. So "how do I find that guy?" – I honestly don't know. Ask around, see if a friend of a friend who knows a guy, who's sister dated another guy who was friend with a guy who knows a developer might not help you out. You're the social media generation, make the most of it. Or start on Codecademy, as you did.
Raise funds to actually pay the developer – I guess this is the part you don't want to hear about. You might wanna scream at me that this is not an option, that you don't have the money, which is why you're offering equity instead. I will counter argue that if you want to play the entrepreneur card, you are gonna need to be resourceful. There are plenty of ways to start a project with limited budget. If you believe in this idea, you should be able to convince others that it's a great idea. If you can convince them, ask them for money. As simple as that. Raise money. It usually starts with friends and family. But! It can also be done online. There are plenty of platforms to raise money, such as Kickstarter for example. Once you have that money, you'll be able to actually pay the developer. There are platforms where you can hire freelance developers, such as UpWork. Its unlikely you'll ever meet the person, and the wages vary depending on location mostly. American developers are expensive. Indian developers tend to be somewhat cheaper, for a certain number of reasons. I know of people who have outsourced in India for big projects, just to make it slightly more affordable. Keep that in mind. Also keep in mind that quality is what you're willing to pay for.
Also, do these types of projects appeal to independent app developers?
Freelance app developers, such as the ones mentioned above? Sure, if you pay them.
With all this said, I'll say this once more: you'll need to be resourceful, no matter what you choose. You'll need to be resourceful should you decide to learn how to program it yourself. This really is the path that I recommend, as you'll learn a great deal, and this knowledge will be tools to be used in your future endeavors. If you're really not that guy, convince someone to co-found the project with you, and work for free, just like you are. Steve Jobs couldn't hack anything together. If Apple exists today, it's plain simply because he had the talent to convince people to build stuff for him. I guess it could be appealing to be that person, however it doesn't come easy. If you want to raise funds, the same pattern applies, you'll need to convince people to believe in you and your idea.
Last, I'll end on this. Would people actually work for equity – with no insurance of ever getting paid?
The answer is yes.
But they'll do it for the Ubers, AirBnBs and Facebooks of the world.
It takes a lot to become successful, but it's not impossible. I've been told that Uber had hundreds of meetings trying to convince people to invest in the idea at first. Look at them now, worth 70+ billion.
So keep at it, be resourceful, and most importantly, be realistic. It won't come easy. Work hard, find ways to get things done, and make the most out of the experience.
Hope this helps, and all the best with Jobronimo!