I've completed my test circuit as follows:

Arduino 

- Digital Pin 5 --> LED Module 1: DIN

- 5V --> Breadboard Positive Rail

- Gnd --> Breadboard Negative Rail

LED Module 1:

- DIN --> Arduino: Digital Pin 5

- DOUT --> LED Module 2: DIN

- PWR --> Breadboard Positive Rail

- GND --> Breadboard Negative Rail

LED Module 2:

- DIN --> LED Module 1: DOUT

- DOUT --> Disconnected

- PWR --> Breadboard Positive Rail

- GND --> Breadboard Negative Rail