Elementary school zones: How likely is it to get accepted to a different school than the one your child is zoned to?

My wife and I are planning to buy an apartment in Brooklyn in and around the Park Slope area (District 15 for public schooling). We have found a couple good options for us but the elementary schools the apartments are zoned for have poor test scores and reviews. While we don't have children yet, we're planning on having children in the next 1-2 years, meaning they'd be starting elementary school in 7-8 years. If we were to buy one of these apartments and the schools weren't able to improve in the next 7-8 years, how likely would it be for our children to be accepted to another elementary school within District 15 that has high test scores (80%+ on ELA/Math) and good reviews? Is there anywhere we can see the out-of-zone acceptance rate data?