Most flash games use Shared Objects to save data, and that should function fine if you download it. However, your downloaded version will not be able to load the online version's save, and vice versa.
If this is really that big of a problem you can get it to work by:
1) Download and play the game offline, and save something.
2) Go to Users/[your username]/appdata/roaming/macromedia/Flash Player/#SharedObjects/
This folder holds all your Shared Objects, but finding the right one can be a bitch
3) Find the Shared Object for the online version - the best bet is to search the macromedia folder for something in the title of the game. You want the .sol file in the right name
4) Find the shared Object for the offline version - in the folder with all the directories there should be a folder call localhost. In there you should be able to find the .sol for the local file.
5) Replace the local file with the online one.
6) Play