Anytime you see a   in the lower left corner of a file directory dialog box in File Buddy used for choosing files, you can click on it to expand the dialog at the bottom. Doing so exposes a text field into which you can type text to search for in names. Clicking the Find button locates the first item whose name contains the text you entered, and clicking the Find Again button locates the next match. The order is determined by the file system, not File Buddy.
The find is restricted to the disk containing the folder whose contents in the list box unless the current folder is Desktop, in which case the search takes place on the disk containing the item last selected in the list.