Isn't it interesting that it doesn't even mention them let alone legalize slavery?
Representatives of Slave States to the Constitutional Convention could have insisted on including it. They could have withheld ratification of the Constitution and thus prevented it from ever being adopted unless slavery was given official recognition. Had they, slavery could not have been abolished, not even by amendment to the Constitution. Had such an amendment been offered, it would never have been ratified by three-quarters of the states. Although outnumbered, there were a sufficient number of slave states to avoid it.
Why didn't they?
The representatives from the slave states to the Constitutional Convention weren't stupid men. They were largely very successful professionals. Most were well-versed in the law. They were smart enough to discern the fact that counting their slaves for the purposes of apportionment in the House of Representatives would give them a legislative advantage. They were successful enough to have three-fifths of their slaves included, but not all. The representatives from the non-slave states were equally intelligent, successful professionals.
“Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons.”
These oversights on the part of the representatives of the Slave States meant that ending slavery was a cultural change rather than a Constitutional change which is why the southern states seceded from the union. They saw the culture changing, turning against them, and the Constitution wasn't going to protect their “property rights” in owning human beings.
In returning to the Union following the Civil War, citizens of southern states had to swear allegiance to the Constitution including the new Thirteenth Amendment abolishing slavery. They refused to accept the cultural change and hid behind a misinterpretation of States Rights for several generations. It wasn't until the passage of the Civil Rights Act of 1966 that they were confronted with the reality of cultural change.
Sadly, morality cannot be legislated. No law will ever eradicate prejudice. There will always be bigots. Fortunately, it is no longer socially acceptable. Thus, it is not the Constitution that is flawed, but rather how some would interpret it.