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She went independent but is still closely aligned with the Democrats, still holds all of her Democratic committee assignments and generally votes with the Democrats -- similar to what Angus King has done in Maine. The difference is King is usually unopposed by a Democratic candidate for his US Senate seat. Sinema, on the other hand recently became an I and already has a Democratic opponent for her US Senate seat.
Everyone keeps thinking she would split the ticket for dems, but an ad campaign marketing her to republicans would do gangbusters, advertise her as the one who “stood up to the dems”, advertise her over the rep choice, split their vote more >

You have to keep in mind there are more registered R’s than D’s who vote in AZ. So, any DEM candidate does not win by just getting the DEM base. They need to win the moderate R’s who they’ve been able to win over in recent times when the GOP puts in crazies like Lake, Masters, etc. If those moderate all go to Sinema instead of the DEM candidate the DEM candidate will be in trouble. 
So, even if Sinema splits off the moderate R’s this is still damaging for the DEM chances. This is the pool of voters the DEMS used to turn AZ blue in recent times. If she happens to get some of the moderate leaning DEMS on top of that (she will) this is really bad news for the DEMS.
Credit to /bobsaget824 >

This seems like flawed logic to me. Even if she is taking votes from the Dem candidate, she is still taking votes away from Rep candidate. As long as Dems know not to vote for Sinema she should draw enough R votes to screw the R candidate over too. Let me know if this is a completely wrong take.
Edit: spelling error >

In Arizona voters are roughly split as follows: 34.5% R, 31% D and 33.7% I. The conventional wisdom for prominent Arizona races is that the I's determine the outcome.
I see no reason (at this time) why Sinema would siphon off enough D or R votes to win. I think a lot depends on the perceived positions of the D and R candidates. 
If the R candidate is a whacko (like Lake), and if the the D candidate (presumably Gallego) is perceived as too far to the left, then I think Sinema would be exactly where she would like to be and would have a shot at scraping I's as well as moderate D's and R's. In a three way race for US Senate in Arizona, the winner only needs a plurality of votes, not a majority. I think this helps Sinema. This scenario seems like a narrow window to me.
On the other end of the spectrum, if both the R and D candidates come off as moderate, then I think it will be a nail biter. Sinema probably wouldn't win but she could hurt the D candidate's chances.
Another factor is how Sinema morph's herself between now and the election. I wouldn't be surprised to see her start pulling away from the D's or at least threaten to do so. Why stay close to them if they are going to fight you in the primary? 
Basically it's too early to see how this is going to play out. Today I favor Gallego as the front runner. I think it's likely he will try very hard to appeal to moderates (even though he a self-proclaimed progressive). I also think the Arizona Rs are nut cases and won't be able to resist voting for a whacko in the R primary. >


I wouldn't be surprised to see her start pulling away from the D's or at least threaten to do so

Did she not literally go independent like a month ago..?