So first of all, which American accent? There's no single accent.

Secondly, if you try to transition slowly, odds are you're going to get made fun of a whole lot along the way for nearly every single American pronunciation you make, because each individual change will stick out more in context. so we're talking about months or years of people thinking you're weird, stupid, or have some kind of speech impediment instead of getting it all out of the way in one go. I have a fairly strong Philadelphian accent, and even here in my home turf I've had the odd person try to make fun of my pronunciation of things like "water" (wooder,) generally it's pretty good-natured fun, but once in a while you get some asshole with a stick up their ass about proper pronunciation. You're setting yourself up for a long time of that, and it will only get worse up until you're actually able to pass as an American.

Third, don't try to be cool, it never works. The coolest thing out there really is just having the right amount of confidence. Trying to change your accent because it sounds cooler kind reeks of trying too hard, like weebs sprinkling way too much Japanese into their conversations for no good reason, or people using big words to sound smarter, or whatever the fuck Elizabeth Holmes does with her voice. It's basically the verbal of equivalent of a neckbeard wearing a fedora (is that still a thing or am I dating myself?)

If you're actually dead-set on changing your accent, the best way is to just live in America and immerse yourself in it and come into it naturally, and you'll pick it up, and then it gives you a solid reason to say how/why you picked it up. You're going to need to spend some significant time here though, months at a minimum, probably years, otherwise at best people will just think you're an obnoxious, maybe naive weirdo who's huffing their own farts about how well-traveled they are, or at worse think you're some sort of weeaboo type obsessive nutjob about America (Google "Rawhide Kobayashi" and you'd get a pretty good sense of how people might think of you)

Last thoughts on the matter, if there's American slang you like, go ahead and use it, but do it naturally, don't force it. I sprinkle all kinds of weird shit into my speech that I've picked up from all over the place, things I've read, heard others say, movies, tv, the internet, but it's never been a conscious choice, it just happens naturally, trying to force it never makes it feel natural. "Stop trying to make fetch happen."