to be able to accomplish this will very specific planning when creating the users table and some hand coding.
you will need to determine ahead of time which columns to allow the user to mark as private.
for each column that will be c=private, you will need another column that will be used to mark it.
for example, lets use the PhoneNumber column, you would need to add PhonePrivate column. If it is to be private, set the value of that column to 1, 0 for public.
the on the results page, add an if statement to check if the PhonePrivate column equals 1:
<?php if($row_RecordsetName['PhonePrivate'] != 1) echo($row_RecordsetName['PhoneNumber']); ?>