Of course the slave trade was conducted under the flag of the US. Importation of slaves to the US was banned in 1808. The first year possible per the Constitution.
The fact that importation of slaves to the US was banned at the first opportunity suggests there were many who recognized the blight that was slavery and they did everything within their power to encourage its demise.
An action in stark contrast to those that created the Confederate Constitution over 50 years later that enshrined the institution of slavery for perpetuity.
Article I Section 9(4) No bill of attainder, ex post facto law, or law denying or impairing the right of property in n-e-g-r-o slaves shall be passed
Where are the "States Rights" much less the human rights in Article I Section 9(4) of the Confederate Constitution?