In flat low back posture, generally the hamstring muscles are tight, which brings the back side of the pelvis closer to the thigh. As the pelvis moves forward, it has a straightening effect on the curve of the lower spine.
Along with tight hamstrings, the flat low back posture will also show strong lower abs, back muscles and weak quadriceps muscles.
While it is good for your back to have strong abdominals, flat low back posture is a deviation from ideal alignment, and affects posture and balance.
The best way to strengthen abdominals is to perform abdominal strengthening exercises.
Kinesiologists call flat low back posture a posterior tilt of the pelvis, as they are referring to the position of the pelvis to describe the mechanism of action that causes the flat low back.
1 Kisner, Carolyn, and Colby, Lynn Allen. Therapeutic Exercise - Foundations and Techniques. 4th. Philadelphia, Pa: F.A. Davis Company, 2002.
2 Kendall, Florence Peterson, McCreary, Elizabeth Kendall, and Provance, Patricia Geise. Muscles Testing and Function with Posture and Pain. 3rd. Baltimore, Maryland: Williams & Wilkins, 1983.