Kentucky, I'm unsure about.
The bridge at Henderson is the big hold-up. No definitive timeline on when it happens, but it's a lesser priority than the new bridges at Louisville and Cincinnati.
Tennessee, I-269 has a planned completion date of 2017, and plus, I-69 already has 21 miles done. So, I'm thinking sometime around 2017 or 2018.
Way off. There's not even a final environmental document yet for the Millington to Dyersburg section. TDOT may get some more of the Union City/Troy bypass section done by 2018 but even that is pushing it. Realistically I see Union City/Troy (SIU 7) being done circa 2025, with south of Dyersburg to Memphis being 2035 or so.
Mississippi's portion is far from completion, but it mostly overlaps routes - US 61 has to be upgraded to be a part of I-69 between Southaven and Rosedale. I-69 finds US 278, overlaps it, and uses the Dean Bridge into Arkansas. The Dean Bridge and US 61 have to be upgraded so maybe 2018 or 2019.
There is no Dean Bridge yet. I'd say mid-2030s at best between Shreveport and Tunica County.
Arkansas is broke and is mostly focusing on I-49, so sometime around 2023 or 2024. Arkansas' portion of I-69 consists of 185 miles, and the Monticello Bypass is the only part of I-69 under construction, hence why the date.
Louisiana's portion means breaking away from US 79 and US 84 northeast of Carthage, heading towards Shreveport. However, I-69 dodges Sherveport and goes around it to the east. As of 2006 (news article dated February 2006 is the source - forgot the name), Louisiana is planning to build it, but is focusing more on I-49. So, 2022 or 2023.
AFAIK, TXDOT says 285 miles out of 650 miles of I-69 are done. With the construction around Houston and Laredo, I-69 could be done sometime around 2016 or 2017.
All of this is wildly optimistic. There might be a continuous freeway from Brownsville to Lufkin in the mid-2020s. Between Lufkin and Shreveport I think the mid-2030s is more realistic.
Now, if pork barrel spending comes back into vogue, the feds and states finally fix their revenue streams for highways, or we decide to throw a bunch of money into yet more stimulus grants, the timeline might improve. But other than that, it seems unlikely.