that you neede to make a low pass filter to make the arduino pwm to analog.
There is a "build in" low pass filter already in the dimmer kit. So, the good news you don't have to do anything, just connect arduino (don't worry to much about polarity, there is also protection "build in", just try one or another way).
The only things I can suggest, if adjustment with kit's RV1 and RV2 would not be sufficient to cover 0-98% range, change resistor R16 (4.7 k) to smaller value 1.0 k.