In order to get David's Jacket, you're going to have to complete the new Over the Edge quest that was added in update 1.6. Head to Megabuilding H4 in Arroyo, in the Santo Domingo district, and look for the little side job icon on the map. This should lead you down an alley with a green symbol painted on the wall and a trash can with a brain dance in it. Use the brain dance and you'll see a brief clip from the Edgerunners series.

The next bit is pretty simple; you've just got to text Muamar "El Capitan" Reyes, who'll tell you a little more about David Martinez and ask you to wait while they gather some info. Just skip time for a day or two and Falco will send you a message. He'll tell you that David's crew has disbanded, but that he's left you a little gift with El Capitan.

After you've spoken to Falco, you'll get a quest marker telling you to head to the Badlands Dam, where you'll find El Capitan. You don't have to speak to them, just head on over to the wall and you can grab David's Jacket from the case. It's not especially great, but it does have some good mods if you like hitting stuff.