Flash Builder 4.7 only supports running on Eclipse 3.7 or 4.2 (not 4.3). The installation is essentially for a stand-alone version now, but after you have installed, you can go into the Flash Builder installation folder (on Windows that will be under "C:/Program Files/Adobe/Flash Builder 4.7 (64-bit)" or "C:/Program Files (x86)/Adobe/Flash Builder 4.7" for the 32-bit version). There is a "utilities" folder with the following program you need to run:
Adobe Flash Builder 4.7 Plug-in Utility.exe
Run that and select your eclipse folder and it should work as a plug-in in your Eclipse. I tested it on Eclipse 4.4 and it would not run. Note, upon running the utility, it will disable it working in stand-alone mode.