Hi Brian,
I guess this "block survey" is a custom plugin (or a 3rd party plugin) you have installed in your site. In that case, you can follow this guide about how to adapt plugins to work in the app. If it's a block plugin then you might want to look for "CoreBlockDelegate" in that guide. This solutions is usually easier to implement.
If you want to include this as part of the custom app's code then it will depend on where do you want that block to be displayed. Again, if this is a block plugin then you want to look for "CoreBlockDelegate" in the app, you will find examples of other blocks but AFAIK right now we don't have any block that sends data to the server. Basically you'll have to include some button and implement the logic to send that data to your WebService/API.
Cheers,
Dani