I don't know anything about Kent, but Lynnwood would be the Edmonds School District. If you get on the district's website, you should be able to enter the address and it will tell you the neighborhood school. If you are looking at 98036 it could be Lynnwood Elementary, Brier Elementary, Hazelwood Elementary, Spruce Elementary or Cedar Way Elementary. Edmonds is a big distirct, there are 24 elementary schools.
If you daughter has been in a gifted program and you want her to continue in a gifted program, I would contact the gifted coordinator ASAP. Getting in will depend on space availablity. She might have to wait. In Edmonds it is called "The Challenge Program" and it is housed at Terrace Park School in Moutlake Terrace. The challenge coordinator should be able to tell you what to do.
In Edmonds, we have "open enrollment" which means you can transfer to another school that is not your designated neighborhood school based on space available. If you don't care for your neighborhood school, you can "open enroll" into another school if there is space. You would have to provide your own transportation.
Good luck!