the cape animation in bedrock edition does not match java edition. Here is a video example:
https://youtu.be/vI9lfKiUHXc

you can see that moving side to side, strafing backwards, jumping up and down all have an affect on the cape's movement. it even oscillates a bit when moving. 

bedrock edition's cape animation, on the other hand, is very sloppy and lazily made. 
https://youtu.be/xZt8iCFRqVM

you can see the difference between the two. player movement only changes the cape's rotation when going forward. After doing some testing, the main query responsible for the cape's animation is `query.cape_flap_amount' which only returns nonzero when the player is moving forward on a relative axis. 

Here is an animation that attempts to correct the animation for the capes to be in parity with java. It looks near identical, but its not perfect:

{
  "format_version": "1.8.0",
  "animations": {
    "animation.player.cape": {
      "loop": true,
      "bones": {
        "cape": {
          "position": [ 0, "query.get_root_locator_offset('armor_offset.default_neck', 1)", 0 ],
          "rotation": [ "math.clamp(-31.5 * (query.cape_flap_amount * 4.0) - math.sin(query.modified_distance_moved * 50.0) * 3.1 - 5.0, -180.0, -7.4)", "query.is_in_ui ? 0.0 : (query.modified_move_speed - query.cape_flap_amount) * math.sin(query.body_y_rotation - query.head_y_rotation(0)) * 38.0", "query.is_in_ui ? 0.0 : (query.modified_move_speed - query.cape_flap_amount) * math.sin(query.body_y_rotation - query.head_y_rotation(0)) * -31.5"
          ]
        }
      }
    }
  }
}