The beach is honestly not the greatest. It is reasonably clean, but it is narrow (especially at high tide) with a lot of trees. Forget about self-launching your kite here; you will need an assistant, or be comfortable drift-launching in deep water (not recommended). This is not an ideal place for beginners.
Changi Beach only works during the Northeast monsoon, which blows from December to March (but not every day, and don't ever expect nuking winds in Singapore). However, when the conditions are right, this is a decent location. Kite sizes to bring would be 12m to 16m depending on your weight.
Drive or take a taxi up Loyang Avenue, past Changi Village, until you reach Changi Coast Road. Follow the road a short distance and enter Carpark No 6 on your left. There is a sign that reads "Changi Beach Park" (Changi Coast Road, car park 6). There is a toilet and a shower house at the car park, and the beach is just a few steps away. The car park can be very crowded when it is windy.
Changi beach is now a well-established kiteboarding area where kiteboarding and windsurfing is tolerated by the authorities, but please use common sense and respect for others to ensure that things stay that way. Please stay reasonably close to the beach and do not ride out into the commercial shipping lane. Also, stay away from the ferry terminal near the south end of the beach, and keep clear of the upwind jetty at the north end of the beach. Doing so will also keep you well clear of the flightpath for the nearby Changi airport Runway I.
Singapore is a major international city. The Changi area is not the most happening, but the rest of the city is only 20-30 minutes away by taxi, car, or public transport.