In the edit.php of profile you should have this piece of code:
<?php if ( bp_current_user_can( 'bp_xprofile_change_field_visibility' ) ) : ?>
<p class="field-visibility-settings-toggle" id="field-visibility-settings-toggle-<?php bp_the_profile_field_id() ?>">
<?php printf( __( 'This field can be seen by: <span class="current-visibility-level">%s</span>', 'buddypress' ), bp_get_the_profile_field_visibility_level_label() ) ?> <a href="#" class="visibility-toggle-link"><?php _e( 'Change', 'buddypress' ); ?></a>
</p>
<div class="field-visibility-settings" id="field-visibility-settings-<?php bp_the_profile_field_id() ?>">
<fieldset>
<legend><?php _e( 'Who can see this field?', 'buddypress' ) ?></legend>
<?php bp_profile_visibility_radio_buttons() ?>
</fieldset>
<a class="field-visibility-settings-close" href="#"><?php _e( 'Close', 'buddypress' ) ?></a>
</div>
<?php else : ?>
<div class="field-visibility-settings-notoggle" id="field-visibility-settings-toggle-<?php bp_the_profile_field_id() ?>">
<?php printf( __( 'This field can be seen by: <span class="current-visibility-level">%s</span>', 'buddypress' ), bp_get_the_profile_field_visibility_level_label() ) ?>
</div>
<?php endif ?>
Between the two hooks:
<?php do_action( 'bp_custom_profile_edit_fields_pre_visibility' ); ?>
and
<?php do_action( 'bp_custom_profile_edit_fields' ); ?>
This will show the option for changing field’s visibility below the field and above the field’s description.
Are you using a custom theme ? I’m asking because all of these is working in the default theme with buddypress maybe you can look at the default theme and see what you miss in yours.