Yes, you can walk from Heacham to Hunstanton along the beach. If you're staying at Heacham Beach Holiday Park, you can walk along the shoreline or the sand dunes until you reach Jubilee Road. From there there's also a solid coastal path which goes all the way into Hunstanton, which is perfect for wheelchair users or pushchairs.
The walk from Heacham to the centre of Hunstanton is around 3 miles and takes around an hour, although if you're just walking up to the amusements at Rainbow Park, it isn't quite as far.