The default Microsoft SharePoint “Search this site” field appearing on SharePoint 2013 sites can be removed by adding the following Advanced Flex Setting with a Setting Value of “False”.
Setting Name: HideSharePointSearch
Setting Value: True/False
This setting is optional. If the Setting is not present, the SharePoint “Search This Site” bar will remain in place but ONLY if the Search is present to start with. If the SharePoint Search is not enabled, then this Setting will not affect anything.