The Flower App collects no information of any sort, and passes none to any external server or any other data management system.
The Flower App may connect to the Google Play servers as part of the installation process as required by Google Play. The Flower App may also connect to those servers if it should need to repair its installation. Beyond this it has no ability to connect to the Internet or communicate with any other installed App or Service on your device.
Information you enter into the App's Search Toolbar is saved within the App as a convenience for your later use. Only the most recent entry is saved, not a complete history of those searches. If you are concerned someone might use your device and open the Flower App and see those searches you should not enter sensitive information there. As a practical note, the only information searched is the content of the Flower App and it contains no sensitive information.