Both have gone out of their way to take independent positions at least on a superficial way, but because both were "team players" in essence their is a ceiling to their popularity.
McCain, for example, did show that he was outside of the 'club' when something big like the ACA is at stake.
However because he is perceived as an establishment guy he has still struggled politically. John McCain is the only person in the history of the United States (that I am aware of) who, after serving as the standard bearer, had to fight like hell (twice) to win his primary against very weak opponents.
As you point out Flake talks a good game but votes with the team. Flake has also become unelectable in AZ. McSally ran as an independent Republican then voted with the team 95% of the time and was unelectable in her district because of it.
So here is the background on the race for the Senate in Arizona. The Republicans had two candidates that led the field; Kelli Ward (extreme right wing nut job) and Martha McSally (first woman fighter pilot, pretends to be independent).
The reason that they needed Arpaio pardoned was so that he could siphon off enough nut job votes so that McSally would win the nomination because Ward was likely to win the primary and get slaughtered in the general, for things like this https://en.wikipedia.org/wiki/Kyrsten_Sinema
The General Election will be like the old yarn about the fat guy (me) and the skinny guy taking a hike in the woods and taking a turn in the trail find themselves in front of a mama bear with two cubs who starts to run at them. They turn and run and the skinny guy starts laughing. "What are you laughing at? You cannot out run a bear".
The skinny guy starts running just a bit faster and yells back "don't have to out run a bear".
You can run as a big party person and a small Arizonan or a big Arizonan and a small party
Martha McSally voted with Trump 97.6% of the time
Krysten Sinema voted with the Democrats 73% of the time (down from 80%)
Sinema is putting together the strategy that will make it easier for more independent and Republican voters to vote for her.
That is how an openly bisexual woman is able to win in a conservative state.
By the way Sinema also didn't vote for Pelosi for Speaker and I am 100% positive that Pelosi was fine with it. In the debates McSally will have to explain why she voted for both Boehner and Ryan when she campaigned on being "independent". Sinema is setting up McSally for the debates.
https://projects.fivethirtyeight.com/congress-trump-score/martha-mcsally/
https://www.nytimes.com/2015/04/01/upshot/the-house-democrats-who-are-voting-with-republicans-more-often.html
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