Field Flux control and Speed Of DC motor
I understood that as we reduce the flux density(B) due to field coils the back emf produced in the armature coil reduces as per faradays law. So Armature current will increase as per KCL applied in the armature circuit. 
  Ea= V - Ia*Ra


OK so far.


  This results for the increase in Magnetic torque on the armature winding due to Lorentz force equation and thus the motor's angular acceleration increases and thus the speed increases.


The increase in torque is a product of the flux and the  increased armature current.


  Thus overall Magnetic flux density in the air gap increase.


No - the flux generated by the armature conductors is tangential to the airgap. It's net effect is to increase the flux at one side of the pole, and decrease it at the other, but the sum of the flux doesn't increase, and due to the non-linearity of the magnetization curve of the lamination steel, may decrease a little. Armature reaction is the term that describes this distortion.



  As the increase in speed is indirectly achieved my increase in armature current Doesn't this make the current in the armature coil go beyond nominal value or rated value?


If you are trying to produce the same torque with the weakened field, then yes, the current will exceed the rated value. Normally the motor will operate at a constant power condition under field weakening, and the maximum torque available will fall proportionally as speed rises, and the armature current will not change much.