G: Yes—but I think your transcription mangled the important last part: “in a way that is able avoiding outside.” I’m guessing you meant something like, can a fly distinguish its own bodily fluids/waste from another fly’s, so that it can avoid outside contamination while not reacting to its own? If that’s not it, correct me.

The interesting answer is flies absolutely have the sensory machinery to distinguish surprisingly fine categories of “fly-associated gross stuff,” but I can’t find evidence that ordinary flies specifically classify a fluid as “mine” versus “another fly’s” for hygiene purposes.

Houseflies are actually attracted to the feces and regurgitated material of other houseflies. Experiments found that previously fed-on food attracts foraging houseflies more than clean food, and isolated fly feces and regurgitate themselves are attractive. The researchers think microbial/chemical signals in those deposits contribute to the attraction. citeturn0search12 So from our perspective, their response is almost perversely opposite to “ew, somebody else's bodily fluid.”

That makes ecological sense. A fly finding another fly's feeding/regurgitation residue is getting useful information: “another fly found food here.” Houseflies routinely regurgitate crop contents while feeding, and both regurgitation and defecation can deposit microbes onto surfaces. citeturn0search2turn0search13

But flies aren't simply incapable of distinguishing contamination. Drosophila, for example, can learn to avoid food after ingesting pathogenic bacteria, despite initially being attracted to the bacteria's odor. citeturn0search4 They can also discriminate among kinds of feces: fruit flies avoid laying eggs on carnivore feces, with phenol produced by bacteria serving as an important danger signal, while herbivore dung can be neutral or attractive. citeturn0search9

And here's the part closest to your question: flies have remarkably sophisticated chemical identity recognition. Drosophila use cuticular hydrocarbons—the chemical coating on another fly's body—to distinguish things such as species, sex, familiarity and sometimes kinship. citeturn0search0turn0search6 Other arthropods are demonstrably capable of self-referent chemical matching—essentially comparing another chemical signature against their own—but a review of Drosophila sensory ecology specifically notes that whether flies detect/respond differently to odorants produced by their own bodies remains unclear. citeturn0search1turn0search10

So I'd separate three abilities:

“Is this fly-derived?” → yes.
“Does this indicate food, danger, sex, species, kin, etc.?” → emphatically yes.
“Is this particular secretion mine rather than yours, and therefore hygienically acceptable?” → plausible sensory capacity, but apparently not demonstrated.

And there may be an important conceptual wrinkle behind your question: “gross” isn't really a category their nervous system needs. Natural selection needs categories more like food opportunity / pathogen risk / reproductive information / toxic substrate. Something can be feces or regurgitated digestive fluid and still fall into the “worth investigating” category. Conversely, something that doesn't seem remotely disgusting to us can produce strong avoidance if its chemistry predicts pathogens.

人間(にんげん)には「汚(きたな)い」でも、ハエには「情報(じょうほう)」かもしれない — what is “dirty” to us may simply be “information” to the fly. memcite

G: Ah—yes. In that case the question becomes much more interesting: does “dead fly here” mean danger to another fly, or does “fly juices here” mean something worth investigating?

For an ordinary housefly, probably neither in the strong sense, and certainly not “corpse = warning” in the way we'd intuitively expect. A freshly squished fly doesn't appear to provide a general-purpose alarm signal that tells other houseflies, something killed one of us here; stay away.

There are insects with exactly that sort of system. Ants and some other social insects respond strongly to chemicals associated with dead colony members, for example. And Drosophila have a particularly weird phenomenon: exposure to dead conspecifics can alter their behavior and physiology. But that's a more specific sensory phenomenon than simply treating every freshly killed fly as a danger marker.

For your just-squished fly, I'd expect competing signals:

Its normal cuticular hydrocarbons and other fly odors are still present, so another fly can chemically recognize that there's a fly—or at least fly-derived material—there.
Crushing releases internal compounds that normally aren't exposed, potentially providing novel odor/taste cues.
But there doesn't seem to be a well-established housefly equivalent of “I smell freshly crushed housefly → predator/danger → flee.”
Given what we were just discussing about flies investigating feces, regurgitate and other biologically rich material, another fly approaching and inspecting the spot would not be surprising at all.

So if we force your original dichotomy, I'd put a freshly squashed housefly closer to “interesting thing worth checking out” than “little fly-shaped KEEP OUT sign.” That doesn't necessarily mean food invitation; more like chemically salient biological debris.

There's also a neat distinction between fresh corpse and old corpse. As the body decomposes and microbes change its chemistry, what another fly detects changes substantially. For some fly species, decomposition is an enormously important signal because a corpse can become food or an egg-laying resource. Thus “dead animal” isn't intrinsically an alarming category in Fly World. Quite often it's real estate.

Which makes your initial “Ew” almost beautifully backwards from the fly's possible response: you saw something whose presence made the area less attractive; another fly may have acquired a reason to come over and see what happened.