We’re going to Europe and we plan to do a lot of walking. I have my eye on some cute flats with trim leather soles. I figure the more flexible they are, the more comfortable they will be for walking. Right?

Oops, wrong.  Feet were designed to walk barefoot on natural surfaces, not in flat shoes on unyielding surfaces.  You will find a shoe with a thicker sole with a bit of a heel lift will stand you in good stead for any type of city or countryside walking on your agenda.  The last thing you want is to be walking in thin soled shoes over cobblestones or brick pavement.  You will feel every seam and pebble.  Also, a shoe that has some type of closure, either laces, straps or Velcro will hold onto your feet better than flats.