Try rest stroking to get the Pickslanting feel. The movement should be a linear like that goes straight into and out of the string.
DWPS can be done many ways- most common is Wrist Deviation, or Forearm + Wrist from a Supinated Arm Position (possibly with Wrist flexion if you try the Gypsy Jazz Approach)
Hey, we updated our “getting started” guide here and I’d suggest checking this out if you haven’t yet done so:
Lots of specific stuff on picking motion; we’d love to hear if you find this helpful.
To be clear the tutorial videos linked in the various pages here are members-only, but I’d say it’s worth trying a month subscription for some more in-depth hands-on instructional stuff on these topics. Even for free though you can read through and get an overview of key concepts / goals, and of course you can also glean a lot from looking at all the discussions and technique critique posts on the forum.
While wrist deviation is one of the most common and fundamental movements, we wouldn’t say that “regular” picking “should” use any particular motion 
All the ones in that chart can work, and we often see them in combination. Hopefully the stuff in the Getting Started guide linked above will help clarify.
As far as how long to be able to do pickslanting…it may take some time to figure out which motion works best for you, but the basic technique should be achievable pretty quickly once you understand the concepts and experiment with various mechanical options. Troy has talked about how it will “click”; it’s largely a question of recognizing when it’s working and trying different things til you get to that point.
And as Troy said earlier, if crosspicking works better for you, feels more comfortable, whatever…that’s great too! I think the main takeaway is being able to identify what you’re doing and whether it’s working. Then take whatever seems to work best for you and focus on getting it as efficient and consistent as you can.