Obviously, kindergarten and public school can go very badly for a highly gifted child. And you will need to be aware of that possilibity, but it can be a good experience.
I would like to be the voice of hope because it does not always go badly. We were extremely fortunate to have a fabulous kinder teacher when my son started school. By the second week, she had him signed up for the accelerated reading program, tested him on the STAR TEST and was taking him down to the library to check out 4th and 5th grade books. She gave him his own math notebook and assigned him problems that dealt with higher math concepts (prime numbers for example). She loved having a student who understood her jokes and made good ones of his own.
They had a special bond and still do. This year, in fifth grade, she invited him to be her aid for the last half hour each day, when his teacher needed to do remdiation with the kids in her class were behind. He was given the choice of working independently on his literature projects in 5ht grade or going to help in kindergarten and he jumped at the chance to help in kindergarten. I know we have been very lucky and many teachers are not like this, but we are in a pretty poor, small town district with a pitiful little gifted program. And then out of the blue we have these fabulous teachers. Who would have thought it possible?
So I guess my advice would be to keep an open mind and not assume either that everything will be fine or that it will necessarily go badly. We did visit the spring before and it made a difference. In fact the other kindergarten teacher (the one we did not pick) refused to let us visit and at that point we knew we would not request her. When I saw the teacher (the one we picked) at work, we knew she was a gem! We went into the fall feeling like we had done a good thing and we were right.