On our preassembled BME280 board the address is set to 0x76, whereas the RGB-Digit Clock expects the sensor at address 0x77.
To change this, desolder 0 Ω resistor R4 and solder it back at position R5.
Alternatively, if you are planning to change the firmware of the clock or (re)program the ESP8266 module yourself and/or don't want to change the hardware of the sensor module, you can change the address in source file "Adafruit_BME280.h" in the following line:
#define BME280_ADDRESS (0x77)
Of course you must edit this line and change the address to 0x76.