Sorry, but I cannot recommend you any remote measurement method on plants because they cannot differentiate flag-leaf and others. It is easiest way to take two dimensions of each leaf, because you cannot put in scanner leaves of many plants at one run. If you worry about leaf shape difference - classify them in different types visually, and add correction depending on the type. We used smartphone-based programs but finally understood that after certain experience visual rating gives a small error, but work much faster.
I would advice you to use any smartphone - based program to measure leaf area in test trial (on limited number of plants), compare results with hand-made measurements (with ruler), calculate correction coeff., and use ruler for other plants. I do it faster. It is based just on personal experience (somebody may have different preference).