Hello and hope you are doing well.
The brown flem could be due to the dissolving clot in the lungs. As you will be constantly monitored with PT/INR test, you need not worry. The dosage of anti coagulants will be adjusted accordingly.
Hope this helped and do keep us posted.
the brown phlegm is probably old blood... which sounds about right if you are on blood thinners (hence bleed easier and longer). Have you been coughing a lot? the lungs are quite vascular so maybe it's just from irritation? Are you sick as well??