There is no separate development kit for the nRF52820 chip. Projects for nRF52820 can be developed on the nRF52833 DK.
For information regarding the differences between ICs in the nRF52 Series, see the comparison table on the nRF52 Series page.
For more detailed documentation regarding nRF52820 development, please see Developing for nRF52820 in the SDK documentation.