Is it possible to have flat feet if you have a really high arch when young?

Yes it is possible. There are multiple reasons for a high arch to flatten out, usually related to problems in the supporting structures such as the tendons, ligaments, bones.
No, but it depends. . If you feel that your arches are high when standing then no they will not become flat. If your arches are high when sitting down then you need to stand to see if your arches flatten out.