Are "flat feet" reversible if you are able to lose weight?

Not reversible. Flat foot deformities are usually not reversible, even with weight loss.
Often not reversible. Feet arches are made of several bones with a strong ligament on the bottom side helping to hold the arch bones together. If a person got very heavy and his weight stretched out his plantar ligaments on the bottom of his feet, and then got flat feet, he might not get an arch back after losing weight. This is because the ligaments may be permanently stretched out and loosened.