I was able to get this to work, although it isn't the cleanest solution. I have a single line text input field for my text entry. When you press enter, this triggers the OnChange property of the text field. This then can trigger actions in other objects and add text to another field, like a chat.
The "onchange" solution mentioned above works or me when running the app a web browser, but does not work in the studio version. I need to press the tab key to trigger the onchange event in the studio version, but loose focus on the text input control in the process which isn't what I want.
The way to do this is to input whatever formula that you would assign to an Icon into the OnChange property of the text input box.
For example, you might have a text input box where the user types in some text. Then you have an icon next to it where the user has to click the icon to launch a search or start a chag. Just take the formula from the Icon's OnSelect property and paste it into the TEXT INPUT BOX'S OnChange property.