I think Kobe will shoot 45-47%.
I see his shot attempts decreasing from 23 FGA to 20 FGA over the season, and the number of shots made per game rounding out somewhere between 9 and 9.4.
His sometimes poor shot selection based on his estimation of his shooting ability (which, though great, is obviously less so now with his age) will persist as Kobe's stubbornness is second to none. However
it will be less reflected in his game and production as Kobe has already showed a willingness to allow Nash to find him easier shots (per the two preseason games the two have played together, and the interviews he has given regarding his altered role).
Also, similar to 2004 when Kobe willingly decreased his shot attempts by 5 (could be slightly more or slightly less) field goals in an effort to properly acclimate the Lakers new talent, I see him shooting less this season - by design and consequence.
Lastly, last year Kobe's FG% dipped below his career average mostly due to the inbalance within the "system" Mike Brown was imploring. Objective observers will quickly recall how increasingly often the Lakers players turned to Kobe as a bailout, throwing him the basketball with less than 6 seconds on the shot clock as a result of their offensive sets breaking apart mid-execution. At 23, Kobe would have no problem creating off the dribble, driving pass his opponent or rising for a jump shot. However at 33, an injured wrist, and popiscle sticks for fingers, Kobe is less productive playing "hero-ball," as it's just too difficult for any player in his mid 30s to be expected to play 1 on 5 with less than 8 seconds left on the clock every 5 times down the court. With the addition of Nash, and the newly added dynamics of a pick and roll offense, Kobe should see less instances of bail-out basketball, which will inherently improve his shooting efficiency.
In all, with the additions of Nash and Howard and decreased possessions as the sole focal point of teams' defenses, an older Kobe should be back around his career average, if not slightly higher.
Just my prognosis