Again, referring to the Declaration of Independence as the source of a right of secession stumbles on the fact that the Declaration affirmed that “all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.” Such a concept is inimical to slavery.
Again every state had slavery at the time of the Declaration of Independence and it asserted that government derives its legitimacy from the consent of the governed and each state could throw off a government that had become abusive toward them and which they no longer consented to be governed by. To say the Declaration of Independence did not support the right of each state to declare independence is not an argument that makes any sense.
Modern people interpret that phrase as referring to slaves. The people of that era, did not. Beyond Jefferson and a few others, the vast majority of people read that as applying to themselves. Specifically to white English descended people who were being denied what they thought was fair representation in Parliament.
This idea that "all men are created equal" should apply to slaves was a later invention, but was not at all the intended meaning when the representatives of all the 13 slave states signed it.
The 13 slave states kept slavery. They didn't get rid of it despite "all men are created equal" being put into the Declaration of Independence.