I've found two ways to integrate a Dialogflow chatbot on an Ionic app.
1. The easiest way
This way can take you maximum 3 minutes to integrate a Dialogflow chatbot, really!
Since Dialogflow exposes a web bot demo, we can simply add an
iframe to show it.
I've developed an example here https://github.com/texano00/ionic3-dialogflow-webdemo-example
2. The right way
I've called "The right way" because this way uses the official Dialogflow client API in order to integrate the chatbot.
Now, instead of having a web view in an iframe, we have the total control of the UI.
So, let's go to an example:
First of all install the library
Here, the full working example using the offical Dialogflow API https://github.com/texano00/ionic3-dialogflow-client-example