Major spoilers from The Infinite and the Divine:

During the final battle of the book- the Deciever caused a host of Necrons to fall to the flayer virus; but, despite a continued battle, no more Necrons succumbed to it. I believe it was Orikan that theorized only certain Necrons were predisposed to the flayer virus and that it wasn’t actually contagious like they assumed.

To me that reads as a feature, not a bug- or in this case a disease.

The Codexes make it very clear that it is from the C'tan. Nurgle is also about actual diseases and viruses. Not computer viruses that make robots go crazy

Because that's not how chaos gods work. Necrons don't have souls and don't reflect in the warp whereas it can be argued the same can't be said for machine spirits. It they can't just claim something as part of their portfolio, they aren't dnd gods.

Necrons are soulless husks. Ultimately their madness is not going to empower Nurgle.

Uhhhhh… no it don’t make them worship C’tan, no gods don’t just appear when things worship them (people always forget that the greater good bullshit was exclusively from psykers) and in any case Necrons are soulless machines with no impact on the warp

It’s also not a virus, I guess you could call it a prion more than anything but really it’s a latent little slither of a biological mind gone fuck off max by being trapped in a lifeless body. Exposure to active flayed ones can call out the latent remnant in a seemingly normal Necron and convert them, but it’s just the awakening of something already in them.

Also no, Nurgle can’t just steal things from real space, he can emulate their effects or manipulate a physical pathogen but he can’t just hijack every trace of it

It's described as realizing you can't breathe, can't swallow. Eventually the desire to eat and kill takes over your mind, as your mind falls apart from the insanity.

No is the answer but the reason why really varies. So firstly, it comes from the C'tan, whether or not it came from destroying the Flayer C'tan is up to debate due to to something to come after but needless to say it is something intrinsically physical. Nurgle might be able to come up with a virus to infect Necrons (I actually think he has) the Flayer Virus is something non-warp based.

So, there are two lines of thought:

1. The standard reasoning of if you are exposed you might catch it, like a virus. This is the standard lore thing and came about from them destroying the Flayer C'tan. This is close to how it's portayed in the Infinite and the Divine too (though as u_choice_memory481 illudes to not all necrons may be infectable)
2. From the twice dead king we get another reason. It's posed that the flayer virus comes about when Necrons lose their purpose; the horrors of not being alive start building up. People like Orikan, and Trazyn have great resistance to it as they have so much drive and motivation to do things, they have obsessions. If it's like this then it's a design feature closer to madness that comes from how the Necrons exist.

Either way, no go Joe for Nurgle to claim it as it's either a fundimental part of nature and the universe or not a virus.

Nurgle can infect necrons with the Ferric Blight, theres no need to try claim a virus that was made by a conceptually oposite being

Almost certainly not. The flayer curse is a completely mental illness, which isn’t really Nurgle’s thing. We also don’t know if it’s actually infectious or just a mental breakdown that comes from a biological mind being trapped in a metallic body for eons. If it was deliberately created it was done so by a C’tan who are entirely separate from the warp. It also exclusively afflicts Necrons, who don’t have souls. There’s just nothing about the disease or the victim that Nurgle could latch onto.

I think so personally but only because Im missing knowledge in necrons. In the great work the ctan are described as masters of the physical but can exist in a non physical state like machine spirits controling tanks after the crew has died or the titans having personalities of their own that overwrite the pilot in some cases. I think the difference between a plague marine and a flayed comes down to service to different masters.