If one forgets to install the fleet from the .zip file download the TCC won't open. Therefore make sure both files from the download are installed and the TCC app should open.
When FS Traffic is fully installed you should see 4 x justflight-FS Traffic folders in the community folder and TCC should open.
Note the TTC also won't open a second time and may take a few seconds to start. It is also possible that it is open but the window is minimized.