Perhaps you should consider a different viewpoint.
An example: A business decides there is a market for 300K cars. Your designer creates a wonderful car. You try to sell it for 300K - and you sell a small percentage of what you anticipated. Is that the designers fault?
The designer is responsible for creating a product that appeals to the customer based on the segment and parameters you specify. You are responsible for determining whether the segment and parameters will meet business objectives.
Now, if you hire an airplane designer to develop a car, then that's a sourcing error / mismatch here. The designer should be focused on meeting the goals (delighting) the market segment / consumer (within defined parameters). Too many times i've seen subjective ideas being pushed as facts to designers (oh, my customer LOVE flashing text and SOUNDS!) without validated, objective proof. The designer is then locked and either has to deliver a sub-optimal experience or walk away from the project.
To be honest, without knowing anything else it sounds like the designer is doing his job. You want to talk to the developer about the actual business end of the app. Your problem is actually a micro of a much larger concern: The vast majority of apps I see look like they were programmed by a designer, or designed by a developer. They either look great with mediocre operation, or perform great with a funky UI. If he's not working with a developer to program this app, you should either pair him up with one on your own, have him/her find one (I recommend one you approve of), or politely thank him/her for their time and find a person/team who meets your needs. I'm speaking from the standpoint of a developer, I love the work designers to and was actually fortunate enough to work for a company for a brief time where I didn't have to worry about the UI, at all .
If the designer is both the designer and developer, and you've vetted their skills, then write yourself down a list of requirements that the initial launch of the app must have. Be realistic with the time frame you want to launch in. Next, give this list to the developer and let them implement those requirements. When they come back and show you a prototype, check your list for the requirements you asked for. Do not release funds until you feel that list was met.
Also, take discipline to avoid scope creep with your requirements. Scope creep is when the customer is constantly adding requirements that 'must' go in before launch, thus the launch is pushed further and further out. Scope creep irritates the developer and you will never have a finished product.
I would recommend you glance at this as a customer just to get an idea of what I mean. Since you want the app developed it would help you to understand some great principles to implement. It's called getting real, and it's free.
I am working with a designer on an app. I am concerned about achievingTo some extent it depends on what role the "designer" has. It's a job title that can cover a lot of different ground depending on the individual involved.
the business goals of the app. How can I be sure to communicate these
to the designer? How much can I expect the designer to contribute to
the business goals in terms of the visitor flow in the app?
For example folk who are mostly pure visual designers will probably be looking for you to define the business goals. Those with more interaction design / content strategy / user research skills will have willing and able to help refine the business goals and make sure the app meets your customer's needs.
Have you talked to the designer about what they are expecting their role to be?