Even accepting this line of reasoning, it doesn't give Lincoln the authority to deprive all the citizens of only one class of "property."
If you are going to make the argument that it was for "Militarily advantageous" reasons, then the capture of all their property which could conceivably affect a military advantage should have been seized as well.
Their horses, their guns, their cattle (for food) and so forth should have been seized. Otherwise the idea that the seizure of their slaves for military reasons was a blatant lie.
At this time in history, the Constitution did not make a distinction between one type of "property" and another, and since it was illegal to seize people's property without due process, it was also illegal to seize their slaves without that same due process.
Of course, by this point in the war, nobody really gave a crap about legal matters, they were just doing whatever they wanted, and then plastering on an ad hoc legal "justification" for what they did. It was all a big game.
The Federal armies routinely seized several classes of property belonging to Confederate civilians. They seized horses, hogs, mules, slaves, houses, real estate. Ask the people that lived in the Shenandoah valley what property General Sheridan seized. As the people of central Georgia, South Carolina and North Carolina what property General Sherman seized.
Whether legal or not is again your opinion. What cases before the courts decided that seizing the property of those in insurrection was Unconstitutional