If your previous period tracking app syncs with the Health app, you can import the data from there. Enable the sync for your app and Health by choosing all the categories you would like to transfer to the Health app. Then sync Health and Flo in Flo’s settings: Menu > Settings > the Health app. After that, the selected data will be transferred to Flo.
To transfer information about your past periods, you’ll need to do it manually via Calendar > Edit period dates > Check your period dates for the months you need > Save.