The relationship between David and Jonathan was certainly the "blood brother" type of relationship.
They made a covenant together.
1 Sa 18:1-4
18:1 And it came to pass, when he had made an end of speaking unto Saul, that the soul of Jonathan was knit with the soul of David , and Jonathan loved him as his own soul.
2 And Saul took him that day, and would let him go no more home to his father's house.
3 Then Jonathan and David made a covenant, because he loved him as his own soul.
4 And Jonathan stripped himself of the robe that was upon him, and gave it to David , and his garments, even to his sword, and to his bow, and to his girdle.
KJV
Does not say specifically that it was a blood covenant.
However the exchange that occurred was common with blood covenants.
David also carried the responsibility of the covenant with Jonathan to the descendants of Jonathan.
2 Sa 9:1-6
9:1 And David said, Is there yet any that is left of the house of Saul, that I may shew him kindness for Jonathan's sake?
2 And there was of the house of Saul a servant whose name was Ziba. And when they had called him unto David, the king said unto him, Art thou Ziba? And he said, Thy servant is he.
3 And the king said, Is there not yet any of the house of Saul, that I may shew the kindness of God unto him? And Ziba said unto the king, Jonathan hath yet a son, which is lame on his feet.
4 And the king said unto him, Where is he? And Ziba said unto the king, Behold, he is in the house of Machir, the son of Ammiel, in Lo-debar.
5 Then king David sent, and fetched him out of the house of Machir, the son of Ammiel, from Lo-debar.
6 Now when Mephibosheth, the son of Jonathan , the son of Saul, was come unto David , he fell on his face, and did reverence. And David said, Mephibosheth. And he answered, Behold thy servant!
KJV
This is also part of a blood covenant.