So, my character has scale mail and a cloak of elvenkind, the scale mail gives a disadvantage on stealth, and the cloak of elvenkind gives advantage on stealth. On my character sheet it shows up as both advantage and disadvantage. How does this work?

If you have one or more instances of both advantage and disadvantage on the same roll, they cancel out and you roll straight. Doesn't matter if you have "more" of one or the other, they don't stack like that. It's simply a case of straight rolling whenever conditions would cause both to be applied.

that makes sense, thanks.

Just leaving the link here for the rule mentioned by @The_Ace_of_Rogues:

They Don’t Stack

If multiple situations affect a roll and they all grant Advantage on it, you still roll only two d20s. Similarly, if multiple situations impose Disadvantage on a roll, you roll only two d20s.

If circumstances cause a roll to have both Advantage and Disadvantage, the roll has neither of them, and you roll one d20. This is true even if multiple circumstances impose Disadvantage and only one grants Advantage or vice versa. In such a situation, you have neither Advantage nor Disadvantage.