How to set a menu link to user/edit in Drupalgap?
When the settings.js file is loaded in DrupalGap, the framework isn't yet aware of who the current user is, so it is not possible to place this type of dynamic link into traditional DrupalGap menus. Instead you can use a block to simulate a dynamic menu.

http://docs.drupalgap.org/7/Menus/Menus_with_Dynamic_Links

/**
 * Implements hook_block_info().
 */
function my_module_block_info() {
  try {
    var blocks = {};
    blocks['my_module_user_menu'] = {
      delta: 'my_module_user_menu',
      module: 'my_module'
    }
    return blocks;
  }
  catch (error) { console.log('my_module_block_info - ' + error); }
}

/**
 * Implements hook_block_view().
 */
function my_module_block_view(delta, region) {
  try {
    var content = '';
    switch (delta) {
      case 'my_module_user_menu':
        var uid = Drupal.user.uid;
        var html = theme('popup', {
            content: theme('jqm_item_list', {
                items: [
                  l('View profile', 'user'),
                  l('Edit account', 'user/' + uid + '/edit'),
                  l('Logout', 'user/logout')
                ]
            }),
            attributes: {
              id: drupalgap_get_page_id() + '_my_module_user_menu'
            },
            button_attributes: {
              'data-icon': 'bars',
              'data-iconpos': 'notext',
              'class': 'ui-btn-left'
            }
        });
        return html;
        break;
    }
    return content;
  }
  catch (error) { console.log('my_module_block_view - ' + error); }
}