"I'm inclined NOT to do [x]." If you say that, an English-speaker will definitely know what you mean, but it doesn't quite sound right to our ears.
You mentioned a different wording of this: "I'm NOT inclined to do [x]." This is better. Putting the "not" BEFORE "inclined" makes a lot more sense.
In English, the word "incline" is also a noun, and it refers to the mathematical angle used to measure how steep something is, like a hill or a staircase. "Be careful, because the hill on that road is at a big incline." So when people talk about how inclined they are to do something, it's a figure of speech. It's meant to make you imagine their body leaning (at an angle, like an incline) towards one option or the other. So it makes sense to talk about whether or not they're leaning towards something, but it doesn't make much sense to talk about how they're leaning AWAY from something. That's just a strange visual. It does convey what you wanted to convey, but it seems out of place.
But everyone knows English always has to be confusing, so remember that there's another word available to you. "Disinclined." It has a very similar meaning to "not inclined." Here's an example of the difference:
"I'm not inclined to go out tonight." All this means is that you don't feel like going out.
"I'm disinclined to go out tonight." If you say this, it means there's probably a reason you don't want to go out. "dis-" at the beginning of a word means the opposite, so this means you're saying, "I am the OPPOSITE of inclined to go out." It has a similar meaning, and it still conveys that you don't want to go out. But instead of a passive lack of interest in going out, you're describing an active interest in NOT going out.
I don't know if that made any sense, haha. But I hope it helped! :)