After Lelouch became the ruler of Britannia, he could have told them that it was part of his plan and used them against, but he decided to just recklessly attack.
Why didn't he incorporated Black Knights in imperial army using the fact that he is Zero after he became king of Britannia?
Well, there are 2 reasons.
Leaders of Black Knights felt betrayed after learning his Geass power and potential usage on them.
Also after trying to kill Lelouch they announced Zero died in battle thus eliminating his chance to announce her Zero identity. Even if they didn't revealing himself as Zero would be a bad move.
to add to JustPlain's answer, there is also the United Federation of Nations.
Before Lelouch was ousted by Schneizel he (as Zero), the United States of Japan, the Chinese Federation and other nations formed the United Federation of Nations.
According to charter's paragraph 17, states that ratified the United States Charter must forever resign their right to have an independent military power of their own. Instead, a supranational military force is created and placed under the control of the Order of the Black Knights, with the condition that all military actions must be approved by the Congress of the U.F.N. before implementation.
Source: United Federation of Nations > Military (First Paragraph)
as such the Black Knights are the Military Power of the UFN who all agreed to resign their own individual military power. for the Black Knights and the Imperial Army to be one entity, one of two things had to happened
Britannia became a member of the UFN and resign it's military. the Imperial Military would most than likely just join The Black Knights but Lelouch would have no authority over it alone
Lelouch would need to take full control and make the Black Knights into the Imperial Army, stripping the UFN of it's military power. this would be like the UFN surrendering to Britannia
