While I think there are some interesting points to be made, your question is unanswerable especially here. The broadness of the topic makes it very difficult to write a full enough answer for you. Also I think you may fallen prey to one of the teleological fallacies of history: the Whig Interpretation of History. Generally speaking Whig History is History that places a lot of emphasis on the movement towards societies that value liberal (not the american social-democratic definition but the traditional liberal) western values such as democracy, republics and personal freedoms. Often those who take the Whig approach will view History as a continuous line leading to the free society that they live in, and often imply that the future holds a freer and more liberal society.

That's where the issue with your question lies, you ask "Why did it take so long for us to get rid of kings and slavery?" with the implication that is was an inevitability. Getting rid of monarchs and slavery happened at different times and for different reasons for most countries. The ideology that drove the French during the french revolution was very different to the ideology that drove the Nasser to overthrow the Egyptian monarchy. While they both had a similar outcome, the Monarch was removed in almost every other facet they are very different. Getting rid of the monarch was the means to achieving another ideological goal. Here is a link to Herbert Butterfield's The Whig Interpretation of History that outlines this in a lot more detail than I can. Just reading his introduction would give you far greater understanding of how to avoid being teleological.

When we look at the issue of slavery, the plantation slavery of the Americas was vastly different to say internal slavery in Africa or even the slavery of antiquity. While they had enough similarities to be both known as slavery, the differences between them are enough to be all be considered very separate entities. Slavery of the Americas was inherently capitalistic and based around ownership of humans. In internal Africa it was based around conquest and lineage making it a very different cultural phenomenon. Furthermore, many societies in Africa were built around the creation of and transportation of slaves for the slave trades. Subsequently the slavery of the Americas was ended very differently to slavery in Africa. While slavery in the Americas was ended through major events such as the American Civil war and the Abolition movements. Slavery in Africa was ended though the start of colonialism. The two can be compared, but are really so different in the ideologies that drove them and their outcomes it would be wrong to say they were the same.

Because of the vast differences between the different types of slavery and monarchy your question cant really be answered. You might have better luck with a question along the lines of "Why was slavery abolished in x(area/country)?" to help with geographical issues. Or you could ask "What made people value monarchs less over time in x(area/country)?" to really get into the ideological changes that made caused monarchs to be overthrown. Most importantly though, avoid assuming that these processes are inevitable, historians always try to avoid teleology.