The kanji Flow app does not collect any personal or private data either directly or through any third party service. No advertising. No analytics. Nothing. Period.
The app does offer quick access to other apps and/or services including imiwa, Google image search, and Kanji Koohii, as a convenience. Those apps and services may or may not collect and/or store personal or private data but kanji Flow does not send them any data besides a plain text string of whatever you request to search for. Please check the privacy policies of those apps/services directly if you are concerned about how they might utilize your personal or private data.