Levi has been writing about this issue in a series of posts, including this one. Flat ethics is generally the intersection of a flat ontology with ethics. That is, how does a flat ontology account for the operation of ethics? And maybe, what ethics, if any, does a flat ontology promote? I'm fairly certain that the answer to that second question is none specifically, though perhaps it does suggest that ethics ought to account for certain considerations (as I will explain below). More powerfully though, a flat ontology has a particular way of describing how ethical practices emerge and propogate.
Now let me see if I can give you a very mundane example.
As I've related here before, I coach my son's soccer team. We are in a league now where boys try out for teams and compete to win a championship. Last week, we found ourselves winning 6-0 about 15 minutes into a 70-minute game. I pulled our strongest players, but we were still up 9-0 at half. In this league, goal differential is a potential tie-breaker for determining the champion, so I suppose there is potential motive for running up the score. But that's just not something you do with 11 year-old boys. At half-time a instructed the boys that only those who had not yet scored that season should really try to score and that otherwise their job was to make good passes. Again, I kept my best players mostly on the bench, and the final score was 11-3. It probably could have been 22-0. And I've seen scorelines like that in my time as a coach, though our team has never been on either end of one.
I suppose you could say this is a simple application of the Golden Rule or even just a matter of manners. While it would be rude to run up the score in a game like this, it is more than a matter of etiquette. Likewise, the golden rule needs to be oddly twisted to operate here. True, I don't want to see our team get beaten that badly. However, the very nature of competition troubles the idea of the golden rule. Do I want others to compete with me for the things I desire? If we take the golden rule as a guide is competition ever ethical? We see this with the child-eating shark example in Levi's post. We see this heavily in political discourses where we talk about social inequities, affirmative action, and so on. However, we can also see it in ecological terms where we balance between our interests as a specieis or as societies versus the perceived interests of other specieis. To what degree is it ethical for humans to dominate the planet and use it for our purposes?
Of course, we can see in all these concerns an underlying requirement for cooperation. In a soccer match, not only must teammates cooperate but teams must agree to play the game within certain rules and conventions, obey the refs, etc. Otherwise, one stops playing soccer and starts doing something else. In a very roughly analogous way, we can recognize interests in human flourishing are tied to the continued health of ecosystems. However, where two soccer teams can appear to agree on the terms of their cooperation, our cooperation with ecosystems cannot operate in the same way. We typically say that such relations are always shaped by anthropocentrism. But that doesn't mean that other kinds of relations might not pertain between humans and nonhumans or among nonhumans.
In fact, we can see that ethical relations among humans always require nonhuman efforts (a la Latour).
In the soccer match, those ethical relations are mediated by a grass field, white lines, goal posts, nets, flags, a soccer ball, uniforms, shin guards, cleats, a whistle, a timing device, etc. They are also mediated by language, which is also nonhuman. In fact, one could (and often does) say that one must compete not only against the other team but field conditions, weather, ref calls, and so on. So in imagining ethics, a flat ontology requires us to see that there is no such thing as "human" ethics. All ethics are nonhuman in the sense that "human" refers to a particular modern, ideological context. As such perhaps it is better to say nonmodern ethics than nonhuman ethics.
In the case of choosing not to run up the score, it is a matter of not being rude and treating those other boys (and their families) with some kindness. However, the potential rudeness or hurt only appears in the context of the game's rules and expectations. In effect, once the game starts to spiral out of control like that, it ceases to be soccer. The decision to not run up the score is a decision to live up to some spirit of the game beyond the literal rules. It is an emergent relationship, not simply with one's human opponents, but with the nonhuman actors in the game and with the game itself as an emergent object.
Applying those lessons to something like ecosystems is obviously far more difficult, but I can try to illustrate the problem with this continuing analogy. As a player or coach, I can't affect the game directly. As a coach I can put players in different positions, suggest tactics, and prepare players in practices. As a player, I can make decisions about how I play. Those decisions participate with others to create the game experience. I can modify my decisions in response, but there isn't a direct relationship with the game only with other actors in the game. The extent to which I realize that whatever decisions I make to win require that the overall game continues, I am engaged in an ethical relationship. A similar ethical relation would exist with ecosystems, though the decision-making is obviously far more difficult.
The central point however is that in a flat ethics there cannot be human ethics. All ethics involve nonhumans as well, and unless one imagines that nonhumans are without agency, then their interests, their ontologies, are already present in ethical systems. This obviously doesn't mean that we do not need to behave differently than we have toward nonhumans. It does, however, reorganize the problem by allowing us to see that our ethical systems are never simply anthropocentric, even if our subjective understanding of those systems may be so limited.