It seem like some applications provide clear labels, icons and call-to-actions that indicate the outcome of swiping gestures while other mobile applications seem to assume a convention or informs the user after they discover the function/feature.
Is there a consensus on whether swiping left or right implies a primary or secondary action? Should it reflect the Okay/Cancel pattern for buttons or be different because the context or convention for gesture interactions is different?
In a word, no. There is no consensus on swipe actions in apps. To illustrate the lack of consensus, here's a quick list of some applications of swipe actions:
(When I say "swipe right", I mean swiping from left to right.)
Other apps
Gestures are generally hard to discover, so they have to be taught and there should be discoverable alternatives for getting to the same features in case the user forgets. (Android's swipe to dismiss for notifications is a special case, as this is a system feature a person will use very frequently and thus is unlikely to forget.) Even Tinder, famous for its swipe gestures, has like and dislike buttons.
There are affordances you can use to help users learn or remember gestures. Lock screen swipe gestures provide good examples. Android uses small icons on sides of its lock screen to indicate what swiping left and right does. In older versions, it used a radiating animation to encourage a user to swipe outwards from a circle. iOS has long used an arrow, a text label, and a repeating animation to indicate how to swipe to unlock. Windows Phone used an animation (not sure what it uses now).
So, if you'd like to implement gestures, make sure to 1) teach them and 2) allow a way to discover them. To reduce cognitive load, you can choose a popular app in the same category (or outside it) and duplicate its gestures, or just one of them. There are no standards yet, but copying what others do creates standards.
Additionally, try to reduce errors and avoid destructive or hard-to-recover actions -- "archive" is always better than "delete". Also, don't introduce swipe gestures where they might conflict with "parent" swipes -- e.g. Android's swipe to switch tabs or iOS's swipe to go back.
Google has something that might help you a lot. You can find the default and accepted general swipe gestures on mobile applications on the following link:
Users are really familiar with this kind of gestures and their actions.
All the gestures are hidden from the user until they either are taught them or accidentally discover them. Gestures have no affordance. Obviously it does not help if app developers don't follow platform conventions.
Onboarding techniques and TV advertising (I am thinking Apple here) can help with education.
From a design perspective gestures should only be used to enhance the experience, but they should never replace the core functionality. Too many apps forget this.
For example, a delete feature should be something you trigger by tapping an icon, but it is ok to also trigger it by swiping in a particular direction.
I agree with Splatz that gestures have no affordance, unless gestures that are widely accepted already by the general public.
Companies such as Apple has created some standards and have advertised those standards to customers. So I think you can safely use those well-recognized gestures, but not on core functions and definitely try not be creative on this.
I found this great article on how to implement the gesture into mobile, that may help you. http://thenextweb.com/dd/2015/11/09/how-to-implement-gestures-into-your-mobile-design/#gref
