What you want to do is certainly possible. Since you're posing this question at all, I'm guessing you're app has the available franchises stored locally as opposed to retrieving them from a server.
Where is the data supposed to be sent to? If you have a server, you can use an HttpsURLConnection and POST the requested zipcode to your server when the user presses calculate or however else calculation is kicked off in your app. You will need the internet permission for this to work.
As a word of caution, you should be very up front about that you're doing this to the user, and also give them an option to turn it off, or even have it turned off per default. Personally, this would be the kind of thing that would bother me a great deal if I were to use your app. (Actually, if I couldn't turn it off, I probably wouldn't use it.)
EDIT
I'm not an expert on U.S. privacy laws but I imagine you probably need a formal privacy statement, as well. You certainly do if your app is also available in the European Union (regardless of whether it's useful there or not - whether or not it's available is enough.)