To me, it just sounds like you say everything all on the same pitch, then at the end of the sentence or phrase you go up or down, then resolve it.
That's not chanting, that's simply reading in a monotone, so there are no tones involved here. Just pick a pitch that's comfortable and go with it. Going up or down at the end isn't necessary either, it's just something certain people do. It's all up to you.
And in any case, there's no need to read in a monotone when you're praying alone at home. You don't even have to read out loud. Whatever helps you pray.