Foreign general aviation (GA) companies who make both international and domestic flights (defined as flights that are used to transport passengers between locations in Greece) are only eligible for VAT exemptions on fuel if they issue a Greek Tax Registration Number and receive a VAT Exemption Document from the respective Greek Tax Authorities. Otherwise, you will be subject to VAT for all your flight activity in Greece, both international and domestic.
Foreign GA companies who do not make any domestic flights (as defined above) in Greece are eligible for VAT exemption. However, such companies are advised to declare that they only do international flights by signing this declaration and returning it to one of the Air bp contacts listed (download declaration here). In addition, if at some point during the year you do conduct such a domestic flight, then you should inform Air bp and obtain a Greek Tax Registration Number to claim VAT exemption.
GA companies are subject to customs control at any point. So, you should be able to prove when asked that a VAT exempted flight was either international or a domestic flight that did not include the transfer of passengers between two Greek locations.