He does not, as he does not automatically get Flat-footed if Blinded
Let us try to analyze that as written, word by word.
A character who has not yet acted during a combat is flat-footed, not yet reacting normally to the situation. A flat-footed character loses his Dexterity bonus to AC (if any) and cannot make attacks of opportunity.
Battle Clarity is:
Battle Clarity (Ex): You can enter a state of almost mystical awareness of the battlefield around you. As long as you are not flat-footed, you gain an insight bonus equal to your Intelligence bonus (maximum equals your warblade level) on your Reflex saves.
The character cannot see. He takes a -2 penalty to Armor Class, loses his Dexterity bonus to AC (if any), moves at half speed, and takes a -4 penalty on Search checks and on most Strength- and Dexterity-based skill checks. All checks and activities that rely on vision (such as reading and Spot checks) automatically fail. All opponents are considered to have total concealment (50% miss chance) to the blinded character. Characters who remain blinded for a long time grow accustomed to these drawbacks and can overcome some of them.
Which means that even though you don't get your Dex bonus to AC while blinded, if you have already acted during combat and/or already react normally to the situation, Battle Clarity does work for you.
There are many entities in D&D 3.5e that seem to be identical or almost identical, or even use almost equal wording, but are not actually completely same. While being blind and being flat-footed both make you lose your Dex bonux to AC, they are not the same.