For the longest time I was using 肉親 for a blood relative however I have seen 血族 being used. I was wondering if I could get more context on the two. I have looked up the individual kanji in the words.
Simply put, 肉親 means your family and 血族 the broader blood relatives.
大辞泉 says it means your parents or siblings. Practically it more often refers to your parents. In some contexts like 遺産をめぐり肉親で争う (conflicts over inheritance among family members), it includes your relatives.
血族 includes your aunts, uncles, cousins etc. So marriages among relatives are called 血族結婚. FYI, not a common word, but there seems to be the word 血族親, which means relatives within 6 steps in the family tree.