Moving from Adobe flex to Air platform

you're mixing different things together

it is not Flex that is sunsetting, it is the Flash Player plugin inside the browser
so yes anything (Flex or not) that publish a SWF file in order to play it in an HTML page in the browser
will have to move to something else

> we need to minimize the migration effort and we are ok to run as desktop client.

then yes AIR desktop is a good candidate

> Is moving to Air is the simplest way, if yes, is there any documentation or support available to do that? 

there are 2 ways you can do it

1. in a desktop AIR app you reuse the HTMLLoader class to host
   your local HTML and SWF file (the one you're currently producing for the web)

  pros:
    - avoid to restructure/refactor your current Flex app
    - use AIR as an HTML host (as if it was a browser)
    - shortest migration effort
  cons:
    - you're dealing with 2 projects now (the AIR host and the SWF content)
    - might feel flaky and/or less integrated
    - probably not fit for longer app support

2. you update and refactor the current Fex projects that produce a SWF for the browser
    to instead produce a SWF for a desktop AIR app

  pros:
    - fully integrated with AIR, you deal with only 1 app
    - AIR desktop now give you full system access and so might allow you

       to do things more efficiently (file load/save, not needing a 3rd party server, etc.)
    - options in the future to also publish AIR mobile apps
    - long time support of the app
  cons:
    - probably have to refactor/update parts of the source code
    - longer process, need to rethink testing, publishing, etc.
    - have to publish and distribute desktop apps (installers, setup, etc.)



for 1. you can use AIR as a host the same way you could use Electron,
the advantage of AIR is that it speaks natively SWF, till AIR 21 the AIR runtime embed a Flahs player plugin,
from AIR 22, you will have to check/install an FLash Player plugins.

I would not advise 1. for long term support of the app, as a quick fix for max 1 year I would say "good enough"
If you do plan to continue developing and adding features and supporting clients using this app, 2. is the way to go imho