I don't program in Flash so I might not be the best one to answer, but if there's any way to run JavaScript from Flash and if you want to be able to upload to different projects where each project is like one chapter of the game and have them communicate with each other, in other frameworks I know it's possible to read and write data to Local Storage to make games interact -- I posted an example demonstrating that here and have source code here. Then the simplest implementation would be to use statements
window.localStorage.setItem(yourKey, JSON.stringify(yourSaveData));
to save yourSaveData to local storage under yourKey from one game and have the other game use
yourSaveData = JSON.parse(window.localStorage.getItem(yourKey));
to read the data. In my code I used
window.open(url, "_parent");
to let each game move the player's browser to other games in the collab -- if you want to do that then you would probably have to publish all the games in the series simultaneously so NewGrounds assigns URLs for them, then once you know their URLs you would quickly edit them in your code and publish an update. (Assuming you don't want to do what I did and leave all the games except the opening game unpublished but viewable by everyone in preview mode.)