Before integrating the app into your flow builder, you need to install the app even you are the creator of the app.
In the above screenshot,
apps with a green label, e.g. "1.0.1" are apps published by others
apps with a red "Draft" label, are apps created by you. Nobody can see it but yourself, until you publish it.
Click the blue "Select" button to view the app:
Great job! Now you can find the app in your Action steps just like any other built-in integration.