I had started crafting this article before the Chase Headley deal, so this might all be moot. But, the fit could be good. Ian Kennedy currently has a year and a half of team control left and is with a team that is obviously in rebuild-mode. They just dealt Huston Street and Chase Headley as nothing more than salary dumps, but they seem to have tightly held on to Ian Kennedy, it seems.
Kennedy was, as you all know, a part of that famous Yankees' draft in 2006 as the 21st overall pick. He did reach the majors relatively quickly, but he only threw 59.2 professional innings with the club from 2007 to 2009. He was then dealt to the Arizona Diamondbacks in the Curtis Granderson three-way trade. He had three decent years with that club, pitching above 100 ERA+ in all three years (last year was partial), including the 137 ERA+ year in 2011.
He was then dealt to the Padres where he was pretty bad, depending on whether you prefer FIP or ERA. In 2013 he pitched to a 4.91 ERA and 4.59 FIP between the two clubs, good for a 0.5 fWAR and 0.0 rWAR. This season has been a bit of an improvement. He's pitched to a 3.62 ERA and 2.98 FIP in 129.1 innings of work. He's certainly not the ideal candidate to work closer to that FIP in Yankee Stadium, but it's definitely possible that he could be a good fit.
Even though Kennedy is a fly ball pitcher, his GB% is actually at its highest level at 41.7%, up about 3% from his career norm. His velocity has also been on an upward trend in recent years (87 mph in early 2012, ~92 mph today), which I think is a huge reason for his success. FanGraphs has his Fastball runs at 16.2 runs, while that number was at -11.4 last year.
I don't think Kennedy would be a magic antidote for the Yankees' pitching problems, but he would be a decent workhouse in the back end of the rotation to fill the Shane Greene/Chase Whitley void. Since he has left the Yankees, Kennedy has thrown at least 180 innings in each year. That's worth something. It would be an incremental upgrade in the mold of Brandon McCarthy--he'll give up some home runs, but he'll also give you decent innings (greater than 9 K/9, less than 3 K/9).
Do I think this deal would get done? Probably not. The Yankees just made a deal for Chase Headley, so I think it is unlikely that the two teams link up again even though they were just at the bargaining table. But if the price is right, they could try to make a deal. I wouldn't give up anything big--definitely not Luis Severino or Aaron Judge. But someone like Peter O'Brien? Certainly. Considering the Padres have said that they might not make him available, maybe they think that they can get more. But if they get desperate to receive something in their fire sale, they might try to get something done. He may not be a perfect fit, but he could provide necessary depth in a starved rotation.