First, find the angle \(\theta\) of the sector using the formula for the area of a sector:

\(\frac{1}{2} \times 8^2 \times \theta = \frac{16}{3} \pi\)

Solving for \(\theta\):

\(32 \theta = \frac{16}{3} \pi\)

\(\theta = \frac{\pi}{6}\)

Next, calculate the arc length \(BC\):

\(\text{Arc length} = 8 \times \frac{\pi}{6} = \frac{4\pi}{3} \approx 4.1887 \text{ cm}\)

Now, find the length of \(BC\) using the sine rule or cosine rule. Using the cosine rule:

\(BC^2 = 8^2 + 8^2 - 2 \times 8 \times 8 \times \cos\left(\frac{\pi}{6}\right)\)

\(BC^2 = 128 - 64 \sqrt{3}\)

\(BC \approx 4.1411 \text{ cm}\)

Finally, the perimeter of segment \(BCD\) is:

\(\text{Perimeter} = BC + \text{Arc length} = 4.1411 + 4.1887 \approx 8.33 \text{ cm}\)