Most Helpful Guy
What do you define as flirting? Are they laughing with each other in a friendly manner? If it's this, then it's not flirting. Is she batting her eyelashes and touching him once in a while? Then this would be flirting.
Don't break up without talking to both your sister and your boyfriend. First, talk to your sister. Ask her: "Why are you flirting with my boyfriend? I do not like that, because he's my boyfriend, and you're my sister. First of all, he's with me, not you. Second of all, it's really strange for two sisters to like the same guy. Stop flirting with him." This is structuring it in a way that might make her see it from a different perspective.
At the same time, talk to your boyfriend. If he is responding to her flirting, then tell him: "Why are you responding to my sister's flirting? I don't like that, because you're my boyfriend, and she's my sister. First of all, you're with me, not her. Second of all, it's really strange for two sisters to like the same guy. Ignore her flirting from now on." If he already doesn't respond to her flirting, and already ignores her, then it's not his fault, but your sister's fault, and you shouldn't be trying to break up with him over the actions of your sister.
If these don't work, try to arrange it so that your boyfriend and sister are never close to each other (as much as possible).