@SILVERisSORRYlegends have basic jump kits attached to their back, you know the one we use to fly. That's why double jump works(it makes the sound too if you pay attention) and why you don't take fall dmg.
In Valkyrie ult, her jetpack overcharges teammates basic jump kit by attaching to them via cords. She isn't dragging you, but giving you some of her power.
But it's a very weaker version of the titanfall 2 jump kit, so it only works in limited capacity. Unless given some boost by legend abilities like jumppad or Valkyrie ult.
(not referring to tap strafe)
