I have not tested this yet but according to the plug-in docs this shoul dbe the way to handle your request.
You will need the Enhanced Search add-on installed and activated.
As part of Enhanced Search you can set a “Pass Address By URL” configuration in your admin panel. Enable it.
With this option turned on convert your forms method from “post” to “get”.
Next change your input field from:
<input type=”text” name=”zip” id=”zip”>
<input type=”address” name=”zip” id=”address”>
When you submit your search request it should add the address field to the URL. According to the documents the Store Locator should then do a search based off of the URL address parameter.