Even if you accept that specific slave trade profits were invested in specific industrial enterprises, the fungibility of capital means that removing those profits would not have prevented the Industrial Revolution. Capital is interchangeable. If a Bristol merchant who invested money he already had in the slave trade later put those returns into an iron foundry, you can draw a line from slavery to industry for that specific investment. But if that merchant had not existed, the iron foundry would still have been built.
The return on industrial investment in eighteenth-century Britain was high enough to attract capital from many sources: agricultural surpluses, domestic trade profits, banking and financial services, land revenues, and investment from continental Europe. Britain’s capital markets were the most sophisticated in the world, and investors from across Europe channelled money into British industrial enterprises. The gap left by removing slave trade profits would have been filled by this alternative capital.
The counterfactual that the reparations argument requires, a British Industrial Revolution that was significantly delayed or prevented by the absence of slave trade capital, is not supported by the economic evidence. The conditions for industrialisation, coal, technology, institutions, skilled labour, deep capital markets, were all in place independently. Slave trade capital was a marginal addition to an already powerful process, not its enabling condition.