By its nature eclipse is quite portable, you can just copy it to somewhere else and continue working. However implementations over eclipse may not be as portable, such as flex builder. If you ever tried to setup already installed flex builder plugin to another eclipse instance, you may have to do manual stuff to achieve.
However there is an easy way;
First check where your current flex builder or the plugin is installed (you can even copy paste the folder from another computer), by default flex is installed under Program Files/adobe on windows and applications/flex on mac.
There is an update site folder just under this directory which can be used as a regular eclipse update site.
Now start the eclipse you want to tie up with flex builder plugin, go to help, software updates. Click add new site and choose local. Navigate to update site folder which we found previously and just select install. Eclipse will download some dependencies, built up links and voila. Here is you old flex working under your new eclipse installiation.
When you boot up eclipse, go and check if flex sdks are ok. The installiation I did on eclipse was ok but on Rational Application Deceloper it was unable to find sdk directories. Since we know the plugin is already located under program files/adobe go point the sdk folder under this directory.
Next? go and start coding with your new eclipse instance..