It was legal in the U.S. and practically all of the Americas for slaves to buy their freedom.

The only place, however, where slaves actually had the explicit legal right to buy their freedom in the unlikely event they managed to save the market price was in certain Spanish colonies, mostly Cuba and some parts of the mainland Americas. Owners had to agree a set fee with a slave, which they would then make a down payment on, and once they paid off this 'debt' they became 'coartados', a higher class of slave who had more rights than normal slaves. If they continued to pay, they could eventually buy their freedom. Obviously, law doesn't always reflect reality and this was routinely ignored, but it was technically a law that existed and some were able to take advantage of it to become free.

But this was not the case in the USA or English colonies as I think you may have been implying.

In the U.S., slaves could buy their freedom only if they somehow got enough money to make an offer that their owner would accept - in effect, they were buying themselves at the market price. All of this hinged on the owner accepting the offer and nothing else, for whatever reason they might have been motivated to do so - either because the slave offered more than the owner considered them to be worth, or perhaps the owner 'liked' a particular slave and wanted to 'allow' them the privilege of not being a literal slave anymore by letting them save up for years and pay a hefty sum of money. This meant that, effectively, slaves wanting to buy their freedom were still completely at the mercy of masters who saw them as an inferior race, unworthy of such freedom - hampering their prospects even further.

In practice this was incredibly difficult, and not just because of the expense, but because the ability for slaves to earn money was heavily legally restricted to various degrees throughout time. In some states it was illegal to trade with slaves at all, in some it was illegal for slaves to accept money for work even with the permission of their owners. They had no legal right to enter into contracts and flimsy to no property rights - their owner could easily just take whatever they managed to save up with no legal repercussions. And even if they did somehow manage to buy their freedom, there were widespread laws that forced freed slaves to immediately leave the state that they were freed from, which would mean they'd need to separate from family and friends to do so - a cost that some certainly didn't want to bare.

In some cases, those who managed to buy their way out of slavery were then able to use their nominal freedom (I say nominal because they were obviously still black in the USA and their ability to earn money was heavily curtailed as a result) to save up and buy the freedom of their family and friends too, but this was incredibly rare. The cards were heavily stacked against them.

Source: Bernier, J. W. (2018). “Never be free without trustin” some person’: networking and buying freedom in the nineteenth-century United States.