I Really Want to Date My Best Friend's Sister

+1 for the above approach, but I would phrase it as a fait accompli, rather than a request for permission: "Dude, I'm into your sister, it seems like it's mutual, I'm going to give this a shot, but I respect you and our friendship too much to do so without giving you the heads-up first." Believe me, if he has a problem with it, you won't have to ask about it it. But you're all grown-ups, and this isn't "The Godfather." You're not asking a favor of Don Corleone, you're giving your bro a fair game warning of intent to date.

 

And another +1

I don't have anything to add. Everyone else is saying what I'd say, and it obvious that you are a man of truth, honour and sentitivity for others' feelings.
If you are the person you appear to be from your posts in this thread, then, whether or not you and his sister go out together, and if so, then whether or not it all works out like roses and bells, your friend is very fortunate, as is his family, and as are you to have had such long term good buddies.

Best wishes.

 

I agree with levite's post. But it sounds like he already indicated he didn't have a problem. Just a thought, you said he doesn't seem protective about her. Do they get along well and actually like each other?
My daughter's friend of several years didn't voice an objection when she started dating the friend's brother. But a rift has now occurred between siblings (why I am not told). Because my daughter is now engaged to her friends brother, that sibling problem has now widened to include her.