Short answer: no. The 13th Amendment of the U.S. Constitution was ratified in Dec. 1865, and it formally abolished slavery (except as punishment for a crime) in any and all United States territories. There has never been any challenge to this amendment via another that would invalidate it (which, under U.S. law, would be the only way to "reinstitute slavery" as you put it).

This isn't to say that fringe parties or organizations in the U.S. didn't try to effectively put African Americans in a social and economic state shockingly similar to slavery: they did (both north and south). Jim Crow laws, Black Codes, the rise of the K.K.K., and institutional discrimination via law enforcement and the legal system kept African Americans at the back of the bus (literally and figuratively) for more than a century after the war's end (and many argue that this still persists to some degree to this day).

[Sources - Doris Kearns Goodwin, 'Team of Rivals'; Jay Winik, 'April, 1865'; Judith Carney, 'Black Rice'; U.S. Grant, Personal Memoirs]

You had sharecroppers, who were given the very very short end of the stick. The land owners, who were more than likely the previous owners of the new farmers, would give them a "loan" of seed and sometimes money so they could start farming, but by the end of the season when the farmer had to give whatever the portion of crop that was stated in the contract was and pay back however much the loan was, he wouldn't have enough to buy more seed and would take another "loan" from the landlord. It was slavery without calling it slavery because most couldn't get out of the loan cycle.

Many would argue that the convict leasing programs that were instituted throughout the South were, as one recent book on the topic calls it, "slavery by another name." Try to picture free labor as a spectrum, wherein, you have slavery--people as absolute property--on one end, and absolute free choice of employment on the other. Convict leasing was a racialized system--it was applied almost exclusively to Black people--and it involved the sale--by local justice systems that used flimsy legal statutes to convict Black people on spurious charges--and purchase of Black individuals--to the users of convict labor--into dangerous workplaces (steel mills, turpentine farms, former plantations, etc) where they received no pay and little investment from the people who controlled their labor. Were people literally property? No. Was racialized labor coercion enforced by the judicial, political, and economic elites? Yes. Was this system instituted in part to meet labor shortages that emerged from the demise of slavery? Yes. So in a sense it was a way to re-establish major aspects of slavery in the new legal regime