Millisecond timestamp (13 digits) in Arduino
18446744073709551615
That 20 digits. It is the maximum value of a uint64_t. Even the Arduino Uno can use the uint64_t. Perhaps the Serial.print does not support it, but the compiler supports it.

Which processor does your RFduino have ?

Where does the timestamp come from ? Perhaps you are asking the wrong question. Perhaps this is a xy-problem.