What exactly did you hope to achieve by using the app on the "blink an LED" sketch?
The problem lies in the fact that your Tinker app just sends out some commands through the REST API. These commands need to be taken care of on the Core. In the factory the Cores are flashes with a Tinker sketch, the same that is being restored when you perform a factory reset. This sketch has the required code to deal with the commands being send by the app.
When you flash your own sketch, you override the factory Tinker sketch, and therefor the code that deals with the app commands. This is why your Core will not respond to any actions you perform in the app, from the moment you overwrite it with your own sketch. You could however add the required code to your own sketch to deal with the commands sent from the app.
The Tinker sketch can be found here. You should be able to extract the necessary code from it and add it to your own sketch.
This might be a very interesting alternative as well, it works great, and is a fantastic starting point!
This thread might prove useful, practically the same discussion:
@Dave (or any of the 
guys for that matter), it might be useful to mention the above somewhere in the documentation, or in the description of the app. It seems as if there's been quite some confusion lately around the Tinker app versus Tinker software. Some explanation of the two might save a few headaches 