There is a health habit called oil pulling, which comes from Ayurvedaic medicine.

This is how I've heard it said on a podcast I listen to on occasion. In this case, I'm not sure if what you have is wrong, but I do like the way my version reads a little better. Though admittedly, that might just be my bias from hearing it that way on said podcast.

You takeput a small amount of coconut oil in your mouth and swish it around, similar to rinsing after brushing your teeth.

By the way, to protect the environment, I don’t spit the used oil into the sink.

"used" is fine here, but it can be omitted. It's typically understood that the oil is "used" since it's been in your mouth.

Instead, I soak it up with used tissue paper and dispose of it.

I didn't make a change here because it could be the case...but is it tissue paper that is used already before you soak the oil? Or do you soak it up with tissue paper, making it used, and then dispose of it? If it is the latter, I wouldn't say used tissue paper. If only because the sentence is just vague enough that someone could read it and think you are putting used tissue in your mouth which sounds potentially unsanitary. Since soak just means that the tissue absorbs the oil, someone could wonder by what action does the soaking happen? Do you soak it by putting the tissue in your mouth? By spitting into the paper? Etc... I hope that is clear, if not I can definitely follow up in the comments.

I’m not sure exactly how much this habit contributes to my health, but since I started, I haven’t had any dental problems, so I think it suits me.

Grammatically, as per usual, there isn't an issue. However, I don't think the phrase "I think it suits me" is particularly common in day to day English. I think a more common way to phrase it would be "I haven't had any dental problems, so I don't see the harm." This means whether or not it is or isn't helping, it isn't actively hurting so you don't mind doing it.

I’m sure the body absorbs a small amount of oil, but I don’t gain weight from it if so.

This sentence and the next feel too definitive when I read them together. I am struggling to come up with a why or without overhauling the sentences when grammatically they are fine. I think the nuance is that personal observations tend to be phrased a with a bit more uncertainty whereas the word choices here are very declarative.

And of course, it doesn’t make me lose weight.

After doing it, I even feel a little more focused and energized.

I think this sentence is a little awkward as a conclusion and actually fits better as part of the section before with the sentence "I’m not sure exactly how much this habit contributes to my health, but since I started, I haven’t had any dental problems, so I think it suits me." If I were to combine it with my earlier comment, here is how I would write that overall sentence. "I’m not sure exactly how much this habit contributes to my health, but since I started, I haven’t had any dental problems, and I even feel a little more focused and energized." I think "I feel something is missing if I skip it." Is a perfectly fine way to end this entry.

Oil Pulling: An Unusual Way to RinsGargle with Oil　油でうがい、オイルプリング

Since "rinse" can be used with a lot of objects, and "gargle" is almost always only used when you're talking about mouth care, "gargle" is better here.

There is a health habit called oil pulling, which comes from Ayurveda.

(or: ...comes from Ayurvedic practices.)

You take a small amount of coconut oil in your mouthorally and swish it around (or gargle it), similar to rinsing after brushing your teeth.

I have been practicing this habit for more than six months.

すごい継続！