Blood clots can skip a generation. If they are in your family, you could be tested for thrombophilia. If a known thrombophilia isn’t found, it doesn’t mean you don’t have a blood clotting disorder. There are many thrombophilia disorders not yet identified. Read more about the genetics of thrombophilia.
Ideally testing is done when not on anticoagulant medication.
In general, testing is only ordered if the family member is in a potentially high-risk situation to developing a blood clot (i.e., major surgery or being prescribed an oral contraceptive). At that point, the family member who had the blood clot should be tested first so others know what to test specifically for.
If the blood clot is clearly provoked (i.e., surgery or oral contraceptives) such testing is not routinely done as it will not change management. If it was unprovoked, testing of the autoimmune condition termed Anti-Phospholipid Antibody Syndrome (APAS) is appropriate as the presence of APAS would require the use of Warfarin as opposed to a direct oral anticoagulant (DOAC). Also, if you become pregnant and have a family history of blood clots you might want to get tested to decide if you need prophylaxis during pregnancy.