Yes, Kimberlin Academy does not take every applicant. By contacting the school itself you can find out more. Personally, I would visit the school. You can see the area, the facilities, and when you speak to someone they can't put you on hold. You probably are already aware of their website http://www.garlandisdschools.net/page.cfm?p=1115
Garland ISD allows students to attend schools that are not the closest geographically, but you have to ask. The Choice of School form lists your preferences for attendance. If possible, your top choice is given to you. Academies are a little different and your child may have to qualify or demonstrate eligibility.
You might also be interested in http://www.gapagt.org