I saw this thread and thought I would jump in to say that sometimes picky eating can be a sign of sensory processing issues. So, do a bit of reading & if any of the other signs resonate then getting your kids assessed might be a good idea.

All that aside, a common strategy to overcome pickiness is to put something you know they will eat on the plate along with a small portion or two of something they may not. Once they've seen it on their plate a hundred times, eventually they might put it in their mouths. The trick here is never to make dinner time about finishing what's on your plate. Just put it on there, and the second the kid eats it, praise like crazy.