Instead of just reading the values of second(), minute(), hour() whenever you need the time, use those functions to set your *own* clock variables initially, and update those clock variable every X milliseconds, with

if( millis() - lastTime > X ){
 lastTime = millis();
 mySlowSecond++;
 // ... rest of your own clock variables updating
}

Then, by varying the value of X below and above 1000, you can speed up or slow down your own clock. Make sense?