Frankly, the issue of King's Bible simply provides West a launching pad in this video for reviving and translating King's issues into the politics and social reality of 2013, which he does very well. But if we pause to think about how he uses King's Bible rhetorically, it's clear that he objects to Obama claiming legitimacy from King's legacy. Ritualizing iconic books legitimizes those who own and manipulate them. By taking the presidential oath on both Lincoln's and King's Bibles today, Obama laid claim to the legacy of both with powerful imagery.
We could take time and space to interpret its significance, but the power of ritual and symbolic imagery lies in making such claims without using words. Obama identifies himself in this way with Lincoln and King. West contests the taming of King's legacy for good reason, but I doubt even his rhetoric has much chance against the legitimizing claim expressed by this photograph.