Firstly complete a thorough visual inspection of the adaptor. If you do not see a class II double insulated symbol, it will be tested as a Class I appliance. The exposed metal parts of the DC jack are often connected to protective earth and can be used to test earth continuity - just be careful with regards to the level of current used for the test as the connection between the DC jack and protective earth may be for functional reasons and not intended to carry high current. Use a low current ('soft test') to be on the safe side.
If there are no exposed metal parts then you can't perform an earth continuity test as it is not relevant - no exposed parts means there is not anything that can become live and be touched by the user. You should record the fact that there are no exposed metal parts and that the test cannot be perform so that in the event of an audit is it clear why there is no earth continuity record for an appliance that is no marked as double insulated.