greetings I need to write a comparative essay on Harry Potter and Huckleberry Finn on the theme "slavery" or social injustice focusing on similarities and differences between the two and applying a literary theory and I was thinking of applying Marxism on both. would that work? and how do I do that?

I think this would work very well. Assuming you are referring to the whole Harry Potter canon, there are several different elements you could bring in when applying a Marxist perspective to your criticism of the text, especially if we are taking into account both slavery and social injustice.
The best way to apply the Marxist perspective to a text is to interrogate it on the basis of how it presents class structures and systems of oppression. We can do this by literally asking questions about a text—for example: what social issues does this work present, and how do these impact the characters? How far do issues of politics, social structures, and economic difference affect the lives of the characters in the novels?
In Huckleberry Finn, we see literal slavery presented in the character of Jim, a black slave who has fled his owners. Alongside him, we have Huckleberry Finn himself, who has also been subject to a different kind of prejudice because of his status in the town as the son of a drunk who is looked down upon by others. Both Huck and Jim are from the lower echelons of society and are looked down upon for different reasons. They each have their own struggles, but at certain points, these struggles converge. Both suffer from economic deprivation.
In the Harry Potter novels, we have literal slavery presented in the form of the House Elves, whom Hermione attempts to free, but, critically, the vast majority of them do not want their own independence. How could we compare Dobby, for example, who does want his own independence, to Jim? What about the fact that Winky is freed against her will and becomes an alcoholic because of her inability to cope? There is certainly a parallel to be drawn between this and the difficulties faced by slaves in the South who, left unsupported after emancipation, did not know how to approach free life.
We can also consider the fact that society in the Harry Potter novels is split between wizards and Muggles; but, within this, there are gradations of prejudice. Hermione, a Muggle-born witch, is termed "Mudblood" by the pureblood Draco Malfoy. Pureblood wizards who marry outside of magical circles, like Andromeda Black, are exiled from their families. How does this interact with the fact that Ron, as a pureblood, is also economically disadvantaged because his family is both extremely large and extremely poor? We could argue that Ron has one form of political privilege, but that this works alongside another form of disadvantage. Meanwhile, Harry, as a wealthy pureblood, has privileges he feels he did not earn, and yet was forced to live in a cupboard in the Muggle world, treated as little better than a household servant. What could Rowling be trying to say in showing how Harry moves, apparently arbitrarily, between these two positions, depending upon the structure of the society in which he finds himself?
I hope this provides you with a helpful starting point. You can find more information about how to apply the Marxist perspective at the link below.
https://infogram.com/the-marxist-perspective-of-literary-analysis-1gg4qpzlr98521y