How can I find the optimum chord wing length for this wing?
You want to fly at the polar point of the lowest energy consumption. If you describe the drag with the usual parabolic equation, you can use the optimum point derived in this answer. It is
$$3\cdot c_{D0} = \frac{c^2_L}{\pi\cdot AR\cdot\epsilon}$$

Induced drag is three times the parasitic or zero-lift drag when you fly at the polar point for minimum energy loss. But the minimum induced drag at a certain speed is also fixed once wingspan and mass are given - you can only mess up by creating a non-elliptic circulation over span, but never get better than this limit.

Now get the zero-lift drag down as much as you can (pick a thin, highly cambered airfoil which produces a high lift coefficient at the given Reynolds number, definitely no Clark Y) and size chord such that this airfoil will work at the optimum lift coefficient.

Note that this will be an iterative process. Picking a chord will influence your aspect ratio and zero-lift drag, so the optimum lift coefficient will be depend on the chosen chord.