I think the OP is trying to get this
So, in short, not flash and not linux
To the OP:
Assuming you can get past your troubles with the download window, you must understand that Windows programs do not run natively on Linux. To have a Windows program run under Linux, you need to install Wine.
But before you do that, you need to check that the application you want to run is supported
by wine. You do that by looking at the AppDB at the Wine project website. Fortunately for you, Star Trek Online appears to work well as indicated by the Star Trek Online page within the Wine AppDB: here
It would be useful for you to read some of the comments left by users to get an ide of how easy/difficult it might be to get wine to work with STO.
So, the next step would be to install Wine through your distro's package manager. Your profile shows "Edubuntu" as your distribution. You should probably be able to install Wine with "sudo apt-get install wine" from a terminal or use the "Software Center" or Synaptic to use a GUI-based program.
The Wine project homepage (which you should take advantage of for documentation if you run into trouble): WineHQ
The AppDB page (use the "Browse Apps" link on the left to get a search window): Wine AppDB
Lastly, you can always search for instructions with Google/Yahoo/Bing/whatever if you have trouble as well. For instance, I found this page