My question is related to the Nasuverse in general.
I was wondering if Shiki is able to kill Servants using his Chokushi no Magan.
In general, yes, the Mystic Eyes of Death Perception (直死の魔眼, Chokushi no Magan, Mystic Eyes of Direct Death) can kill Servants
Beings will have different amounts of lines depending on their complexity. Humans will have a countable amount in geometric patterns. The Dead have numerous lines all over their bodies that make their appearance hard to discern. Members of the Phantasmal Species will have very few "parts vulnerable to death." Those without physical bodies like Servants are also able to be killed.
This comes from the TYPE-MOON Fes. Official Pamphlet 10th Anniversary Q & A Booklet which is citation 14 in the section I linked to
Q: Since Saber and Gilgamesh have physical bodies in Fate/Stay Night, can Shiki see lines on them? (@LestatDusk)
A: Not just when they have a physical body, the Mystic Eyes of Death Perception are effective even when they're in spiritual bodies. For Shiki [Ryougi], if the opponent can be recognized as "living" (not "life", but "live"), she can see the lines of death. For example, the ghosts in Overlooking View were dead, but they were "living" in the sense that they can interfere with the current world. Also, why she didn't succeed against the Sarira in Araya's arm is because it belonged to an enlightened one who achieved "becoming extinguished, alive." To kill it by the lines of death means she has to decipher advanced "lines of death" levels higher than the normal concept of death. But what's sad about bones is that rather than having to do that, they'll turn into ash if you burn them. If you have time to be using Death spells, level up and beat it physically.
Source - Citation Note 14
Of course, whether the user can do it is another thing. In the Q & A quoted above, the answer seems to assume that "Shiki" refers to Ryougi Shiki. If we are talking in terms of Tohno Shiki, then it'll be a bit more difficult due to the migraine he suffers from when he takes off the Mystic Eye Killers glasses Aoko gave him.
The Mystic Eyes of Death Perception are not infallible. The human mind was not meant to perceive death in such a way, and using it is highly taxing on the human brain, causing headaches. In addition, there are multiple levels of perception; in the beginning, Shiki could only see lines on people and objects, then progressed to seeing dots on living things, then dots on inanimate objects. Each step takes the mind further from natural perception, and each step is more damaging to the brain; eventually the stress leads the brain's blood vessels to burst and death for the user.
Soruce - Tohno Shiki: Abilities 5th Paragraph
Ryougi Shiki is not shown to have migraines from the use of her eyes. Also,
Lastly, the ability to perceive and trace lines or pierce dots does not give the user any added physical capacity to perform the task itself, especially against an unwilling target. [Tohno] Shiki must still get in range, aim, and move his hand by himself, which is not a trivial task against the kind of enemies he faces.
so even with his Mystic Eyes, Tohno Shiki must still be able to stand against a Servant and as mentioned in Ryougi Shiki's page:
[Ryougi Shiki's] combat ability is only possibly around the level of Ciel, allowing her to manage a defensive fight against a being on the level of a Servant. While still much stronger than [Tohno] Shiki, who holds no hope in even competing with a Servant defensively, it is unknown how her abilities work and the speed with which they take effect should she choose to utilize them. She is noted to be the second strongest being in the Nasuverse when not including Servants, under Arcueid Brunestud and above Primordial Demons.
Source - Ryougi Shiki: Third Personality
Tohno SHIKI/Michael Roa Valdamjong on the other hand, while he has Mystic Eyes, they are not the Mystic Eyes of Death Perception (though he believed they were the same) and he is only cutting the "life" of a person and not the "death", which is what Ryougi and Tohno do.
I should also point out that while the Mystic Eyes can kill a Servant (given the user's own physical skill), not everything can be killed with them.
The only entity [Tohno] has failed to kill is Night of Wallachia, since it does not exist as an actual being, but instead as a phenomenon that does not "exist" until it occurs. Nasu has also stated that beings such as ORT are immune to Shiki's Eyes, having no concept of "death" in the first place.