If Flake supports Kavanaugh then it is proof that he intends to run for office again in some capacity. If he did not intend to run again for something, there would be no reason for him to betray his Democrat friends, colleagues, and family, since he is retiring from the Senate anyway.
But, he could be doing a McCain tactic. McCain was famous for telling Republicans that he was going to vote with them only to stick the knife in the back at the last minute. He seemed to actually enjoy doing this. Maybe Flake is following his mentor's example and never planned to vote for Kavanaugh.
No, I think Flake is just doing the right thing, he comes what has historically been a very red state, Sen. Lindsay Graham too, certainly made an emotional appeal to Flake, Lindsay being McCain's cohort.
Also, there has to be some cooperation some time, some reaching across the aisles, even Barry Goldwater said that.....yes, we want a Conservative agenda, if I can find some picture of Tip O'Neill and Reagan together, it doesn't mean Reagan betrayed conservative values.
There is enough gridlock as it is and under Obama, it was nothing but gridlock for the last 6 years.