Kazanluk Thracian Tomb (the original) can be visited by ordinary people if they pay and schedule ahead their visit. Talk to the local guide and ask for the process. Otherwise, there are several travel agencies which already obtained the permit through the Ministry of Culture and include the visit to the original in their tours.
Please also keep in mind that the frescoes in the original are very sensitive to temperature and humidity changes, so the visitation is controlled. We want to preserve this wonderful piece of architecture and art at least for the next 2500 years, as it was preserved till now.