Somewhere around 4500mg EPA and 3500 DHA, but you would want to work up to it to make sure it sits well with you.
If you are going to take an anticoagulant, you wouldn't want to take such high doses, maybe just 1-2g total, if any, so you have some antiplatelet support as well as anticoagulant support. But as
@andyguitar points out, you would want to let your doc know. The PT/PTT test, which is the standard test for measuring how thin the blood is and monitoring warfarin therapy, only picks up the thinning influence of the coagulation portion of blood clotting, so if you are also taking something that influences platelet aggregation, your blood may be thinner than reflected on that test.
Similarly, taking nattokinase with anticoagulant meds can also lead to blood that is too thin.
If you are thinking about low dose anticoagulant therapy instead of the doses used for thrombosis, you may have to go with warfarin. Not sure if there newer drugs come in a low dose option.