Great comparisons. They draw out some key distinctions between earthly and heavenly kingdoms that many Christians fail to see or actively blind themselves to. 

But when you say,

I pledge allegiance to the true Commander in Chief, and to
the kingdom for which he died, one church under God, indivisible, with
God’s freedom and justice for all.

Its an ugly mix.  But more than that, calling Jesus "Commander in Chief" is like calling George W. Bush "Jesus," as some American conservatives once acted.  They both sacrilize aspects of the American state and constitution.