Your method is wrong. JUST ADMIT IT!
He starts off by telling us he doesn't have the numbers to back up his claims - "I don't know how high the sun is" at 0.43, so he has no concrete mathematical basis for this argument.
He also gives us a hint at his own perspective (heh) when he concocted this theory - "it makes you start to doubt, but I know it's wrong!" at 1.46.
Sorry, but just drawing lines with a vanishing point at the horizon doesn't stop the fact that the little circle that's meant to represent the sun still drops BELOW the horizon in that big proofy diagram at 2.40 and again at 3.32.
Even with the perspective lines, where is the sun supposed to go once it hits the vanishing point?
And If it traces a circle over the earth, we should see it describe a large arc of a flattened ellipse, reversing direction before reaching maximum distance from the observer, and the continue going along the same circular track in the sky. With these perspective lines, as any middle school art student could tell you, such a circular path has to stay on the same side of the vanishing point.
Especially damaging is the "photo of reality" he shows at 2.51 to support his view - no single line above his yellow horizon line ever goes below or even touches the yellow horizon line. This literally makes no sense when you are talking about an object that appears to recede below the horizon.
He uses this photo that was taken at, maybe, a 45 degree angle from "straight on" and slaps it over a diagram shown from a 90 degree, "straight on" perspective to show how it's wrong.
This would be the equivalent of me taking a picture of the Empire State building at ground level, overlaying it on a picture if the New York skyline and claiming that the building in question was actually a pyramid, because it clearly looks different in my photo.
The crowning jewel is that at 3.30, when demonstrating his perspective proof, the puts the sun on a line below the horizon - this line is not in line with the vanishing point he so graciously provided, so the sun would have to reach thay point, cross it, and continue on its path - this is completely incompatible with his explanation of the motion of the sun if it's orbit is parallel with the plane of the Flat Earth. Either it has a different vanishing point and is not parallel or it is not on a straight line path - these are the options here. His diagrams illustrate this beautifully.
He also seems to forget to follow his own lines and make the sun shrink as it follows it's perspective lines into the distance. Again - middle school art class.
And before you bring up the atmospheric projection thing, there really needs to be some consensus on the height of the sun, it's orbital characteristics, the speed of light and the refractive qualities of the atmosphere before that argument is made.
At 4.15, he basically ends up proving our point.
"Look at these lines! They're parallel!"
Well done, p-brane, they are - and I think you will notice in that picture of those lovely rows of flowers that at no point do any if the rows touch or go past each other. Even if that were an infinite field of flowers, none of those rows would ever touch or cross each other, let alone your "z-axis" - so if the Sun is on a parallel path to the Earth, then the only way it would meet the horizon would be if both the Earth and the Sun's path were infinite.
The rails in this photo, for example:

They don't touch at the vanishing point and then keep going, crossing over and continuing away from the observer on the same lines.
If you want to employ a vanishing point at the horizon, you have to treat it as such - a convergence at infinity. It is a limit - a theoretical end point where, if you extended those lines are far as they would go were they just lines on a plane [i.e. forever] they would meet.
The rest of the video is more or less a sequence of these overlaid diagrams that succumb to the exact problem that he sats the creator of the original diagram had: his diagram doesn't represent perspective accurately.
At 6.50, he says the spherical proponents "don't understand perspective! They don't get it!"
Sorry, love, but I'm fairly sure there's far more that you don't understand about perspective - you even made a video about how little you get it.
My favourite part, though, is a comment (that I will try and post a screenshot of as soon as my phone starts to co-operate) addressed to user setecordas from p-brane himself, stating that "the sun is immune to the type of perspective most of is are familiar with."
...you mean it doesn't follow the conventional laws of perspective that you based your entire argument on? Oh. Ok, so nothing you said actually meant anything? Not even the picture with all the pretty flowers?
This makes me sad.
So no, I will not just be admitting it works until you admit the Sun is a giant, phosphorescent fried egg in the sky being pushed around by the headless ghost of Lucille Ball every day.
As I can see, both arguments are just as mathematical as each other.