Just change the Visible property in your FeatureLayer.
public void AllToggle(object sender, EventArgs e)
{
CheckBox ckbx = sender as CheckBox;
if (ckbx.Name == "AllAvailable_Checkbox" & ckbx.IsChecked == true)
{
MyMap.Layers[1].Visible = true ;
}
else
{
MyMap.Layers[1].Visible = false;
}
}