There is more to this construction project. In addition to a new higher flyover, the existing flyover will be completed, plus both east and west I-40 bridges over the Wolf River just east of the flyover are to be totally replaced, with additional lanes. One estimate I have heard is 4-5 years.
The 385 loop from I-40 MM 24-25 is complete to Collierville, and connects back to I-240. Please note MapQuest has not updated their maps-last section of 385 was opened in Nov 2013. Continue on 240 to either I-55 South to Mississippi, or continue west to cross into Arkansas via I-55 or I-40.
If you elect to drive thru the construction zone (I-240/I-40 junction) try to avoid rush hour if westbound in the morning, or if eastbound, in the afternoon. Traffic typically backs up close to 20 miles on I-40 at rush hour.
Construction just started in Dec 2013, and is not too bad as of now, but expect greatly increased delays as construction ramps up.