There is a less complicated approach. All that is really needed are the three equations of motion in a single linear dimension for a body under constant acceleration starting at rest, relating the acceleration(a), velocity(v), distance(s), and time(t):
1) v = a⋅t
2) s = ½a⋅t²
3) v²= 2a⋅s
Recognize that this is a constant acceleration situation: the incline is straight & at the same angle, so gravity exerts the same force on the object (parallel to the incline) at all positions; air resistance is negligible; rolling resistance is assumed to be constant. So the same force acts on the object at all times; therefore the acceleration is constant.
The situation is that an object rolls down an incline, converting potential energy to kinetic energy, while losing some of the potential energy to friction. Measuring the height of the incline gives the total potential energy. Measuring the total distance traveled down the incline, and the total time of travel, allows for calculating the constant acceleration parallel to the incline and the final velocity (also parallel to the incline). With the final velocity, calculate the kinetic energy. Energy lost due to friction is the difference between the initial potential & final kinetic energy.
Note: If the final kinetic energy is greater than the initial potential energy, I want to know your secret!