Not really worth the trouble. If you use floursecent tubes, they have flicker too, and the colour may not be accurate. The brightness may be too low/high as well. Commercial lightboxes and lightpanels are calibrated to a 5000-5500K colour temperature and the right brightness.
Bear in mind that white LEDs are not exactly neutral, their colour temperature is not correct and the brightness may not be correct either. If one is serious about your work, don't stinge on the lightbox and loupe. If building one, get the 5000-5500K flicker-free floursecent tubes with the correct brightness. It's critical that you view slides with the correct brightness and colour temperature or you'll never detect your over/underexposure and any colour casts.