Viewers discuss why characters scream in reaction to learning about blood transfusions in the episode, with one explaining it as a common comedy technique called the "secondary scream."
When Kramer tells Jerry that he's got "three pints of Kramer in him," Jerry starts screaming hysterically. I understand why Jerry started screaming, but why does Kramer scream? Also at the end when he found out that he had Newman's blood in him, Kramer and Newman started screaming as well. Is there any reason for it or am I making a big deal out of nothing?
This is a common comedy schtick that I have once heard referred to as "the secondary scream"--someone looks at someone who is not aware of their being frightening and screams, then the person being looked at screams because of being shocked at someone screaming at them. It was done in "E.T." with Drew Barrymore (shortly before she started drinking), and I believe the earliest recorded instance of this is in "Bride of Frankenstein," when the monster meets his frizzy heared bride. She catches her first sight of him and she screams, causing him to return the scream, etc.
As to why the ending, as you recount it? Lousy, lazy scriptwriting. I knew there would be a scene in which Jerry "freaks out" as soon as he told Kramer that he'd freak out if Kramer's blood entered the apartment. I also anticipated the "blood brother" scene.