In regards to the first question in your post about researching and picking a school, I think that the more you can find out about how flexible the administration is, the better sense you'll have of how willing they'll be to work with your child to meet his needs. Ask how they handle children of differing abilities in a classroom. Ask specifically how they accommodate gifted children. Ask if they ever accelerate by subject if it's needed. We picked our school because the administration touted their flexibility on our initial tour (breakout groups by ability across the entire grade for both reading and math, and subject acceleration when needed).
Regarding the start-of-year conversation with the K teacher, I think different schools, and teachers, have different philosophies regarding parent input. I don't think the advice to sit back and let the teacher discover your child's gifts works in all cases; I think it depends on the school, the teacher, and the child.
For us, we have a DS who won't show what he's capable of early on, and we have a school that values parent input. So we've talked with our teachers about a month into the year in both K and 1st grade, and it's led to great outcomes. The parents of the another gifted child in DS's grade took the sit back and wait approach, and the teacher never did anything until they finally spoke up and asked for subject acceleration in March of his K year. Even if you have a clueless teacher, a flexible school creates an atmosphere where parent input is more valued, and it can be easier meet individual students' needs.