Who is the alpha?

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Danny. Kenickie is Second

Kenickie's the leader.

I always got the impression it was fairly 50/50 between them. If I had to choose I'd say Kenickie though for two main reasons. Firstly he was going to be the one to drive in the drag race before he got hit on the head.
Secondly he's dating Rizzo, the "leader" of the pink ladies.

I never even questioned the fact that Danny was the leader. It always seemed obvious that he was and that Kenickie was the number two guy in the group. Although the T-Birds probably didn't have an official leader like in A Clockwork Orange where Alex ruled over his droogs and punished them if they got out of line. It's just that Danny was seen as coolest guy by the other kids and the one that everyone looked up to. He was like the center of the group and everyone gravitated to him and around him.

Danny and Kenickie were best friends and I don't think they worried about which one was the leader or who outranked who. However there are a few scenes where Danny shows himself to be the more dominant personality. For example, early in the movie they are about to enter the diner and Kenickie asks Danny if he was still thinking about "that chick".
Danny denies it and seems to get slightly annoyed. Kenickie says that he was just thinking, Danny tells him not to think so much and pushes him into the diner. Granted, it's a good natured, even affectionate scene, but it shows that Danny, even in friendship, is the boss.

Kenickie was dating Rizzo, but simply because she was the leader of the girl's group, doesn't make her boyfriend the leader of the males. Not to mention, Rizzo and Danny did date at one point, but broke up for reasons that were never mentioned.

The reason that Kenickie was originally going to drive during the race was simply because "Greased Lightning" was his car and he'd always planned to race it. He mentioned it to the gang as soon as he got it: "I'm racing her at Thunder Road."
Danny, being his best friend, wanted to show that he was there for him, so he agreed to be his second, but this was only in terms of the race. In life and in the T-birds, Danny was the Alpha and Kenickie while definitely cool, but still the Beta.

Rizzo.

Definitely Travolta, he got with the hottest chick (Sandy)

There may be different answers depending on whether you're talking about the movie or the original play. For the movie, they gave a lot of Kenickie's lines and songs to Danny.