Moved to the Flash Pro forum. They will be able to help you here.
You can use the online file storage in the Creative Cloud and then download the file onto another computer. You can also set up Creative Cloud Connection on two computers and be able to sync between them and the online file storage.
I have no familiarity with the cloud. If you have a file that was created in an older version of Flash, it should be editable in any version from that older version to the present.