We had success in K, but there were two factors working in our favor:
1) a really good teacher, who "got" our DS and wanted him to learn and grow. Do not underestimate the power of a caring, unthreatened teacher. She is why I know that DS6 is HG+, because she requested testing. I knew he was GT, but I thought he was MG. She was wonderful!
2) a mostly non-academic K class. I know that sounds odd, but it really helps if what the kids are doing is mostly playing and exploring and FOK stuff, rather than learning letters and numbers (etc.) that they already know. The more academic the curriculum, the harder it is for the teacher to give an HG+ child what s/he needs intellectually.
1st grade was when we hit the wall, and we hit hard because we had a highly academic curriculum and a teacher threatened by DS's intelligence who was unwilling/unable to differentiate the curriculum and who immediately made it all about her. It became clear very fast that DS could not thrive in that classroom.
Look for a mostly play-based, social curriculum and a teacher who is sympathetic to GT kids. Good luck! I hope you find something that works for you!