Is “how much am I owing you” grammatically correct?

The only correct answer here is from Andrew McKenzie; however he has left it a bit brief, and I’m happy to elaborate a bit more.

English divides verbs between dynamic and stative. See Stative verb – Wikipedia.

Dynamic verbs are verbs that can be put in the progressive (be doing); stative verbs normally cannot.

So “how much am I owning you”, and for that matter “how much am I owing you”, are not normally grammatical in English, because own and owe are both stative verbs.

However, that ends up saying that you can’t put own or owe in the progressive, because neither are verbs that you put in the progressive. Let’s tease this out a little more.

Dynamic verbs are verbs that describe actions or activities, something that happens in the world. Stative verbs describe states, situations that just are.

Actions and activities are situations that perceptibly start and stop, and can keep going on, and can happen just for a little while. For that reason, it is meaningful to speak of a difference between ran and was running, or walks and keeps walking.

States are not situations that perceptibly start and stop, and do not happen just for a little while: they just keep going on. For that reason, it is not meaningful (normally) to speak of a difference between knows and was knowing, or likes and keeps liking. They are states that already have built in the notion of keeping on being true.

Owning something and owing someone something are taken in English as states, not actions. They’re not stop–start, they’re not something you can do for a little while or continuously: they are ongoing states, just like knowing or believing or hearing.

Now, some verbs are dynamic though they look like states. Sitting and sleeping for example. And some verbs are stative though they look like actions. And you can reinterpret a verb so that it turns from one category to another. You hear noises, you are not hearing noises; but you can be hearing rumours about me, because that kind of hearing is more about gaining intelligence than sensory perception. On the other hand, Franciscus Alex Rebro’s example of I’m owning you in this game works, because that sense of own is not a state of possession, it is an action of defeating someone.

So the grammatical division between the verbs is leaky and contextual. But by default, both am owning and am owing are ungrammatical in English, for reasons of both verbs being perceived as states.