Mixolydian is correct in saying that either could work, with the correction of verb choice. It's probably worth elaborating what the difference between the two is, where the passive voice comes into it, which would be better, and so on. In this example, the two expressions are effectively equivalent. However, they are not entirely equivalent, and in other situations the difference may matter.
The final part, "in the system", is consistent between the two and isn't involved in any difference. In both cases, it is simply providing a location for the activity described by the verb. As such, I won't refer to it in setting out the difference.
This leaves us considering the difference between "input did not flow" and "input was not flowing". These are two different ways of referring to things in the past. There are others - "input had not flowed", for example - but for now let's just think about those two.
They are both in the negative, which can confuse things a little. In the second case, it is clearly the negative of "input was flowing". In the first, however, it could be the negative of "input did flow" or "input flowed", which are different grammatical constructions that emphasise things differently. Really, you could negate "input flowed" as "input flowed not", but that would seem archaic; people will generally negate "input flowed" as "input did not flow". So let's look at the positives, so the negative isn't confusing things. This gives us:
1: "Input flowed"
2: "Input did flow"
3: "Input was flowing"
The first is the usual form of the simple past, or preterite. This simply describes an event happening in the past, with no further implication. The second is an alternative form of the simple past that is mostly used either for negation (as the usual way to negate the simple past is to do "did not" followed by the bare infinitive), but is also used for emphasis - if someone says "I think it didn't flow", you might respond "it did flow" to emphasise the contradiction.
The third is the past progressive, and in the sentence as you give it this has no practical difference from the other two forms. The simple past indicates that a given thing happened in the past (and that's an example of the simple past in itself), while the progressive indicates that it was happening (again, that's another example). The progressive aspect indicates an ongoing process, while the lack of the progressive aspect allows the possibility that it was a simple, atomic event rather than a process. Pretty much any action can be progressive or not, but where it matters that the action was ongoing you should use the progressive.
To illustrate with your example, if there were a single piece of input that didn't flow, it might be better to say that "that input did not flow into the system". If input in general were not flowing, it would be better to say that "input was not flowing into the system".
(You may notice I changed "in" to "into"; that may or may not be better, it depends on the details, but it would be what I would more expect to see. "In" implies that the input gets into the system, but then got stuck, while "into" suggests that the input never actually got in the system.)
You also mention the passive. In this case, neither is passive. "Flow" is intransitive. "In the system" is an adverbial phrase. Intransitive verbs cannot be passive. A passive constructions is where a transitive verb lacks a subject (though the subject may be supplied by an adverbial phrase). Thus "the bear was shot" moves what would normally be the object of a sentence to become the subject, uses an extra verb for which it is the subject, and uses the original verb as the object of the new phrase. "The bear was shot by John" is "John shot the bear" in passive voice, but we can leave off the adverbial phrase and leave the matter of who shot the bear ambiguous.
In the case of "flow", there is no object. "Was not flowing" is not a passive construction, but rather has the original subject of a present tense, the verb being "to flow", in a past progressive form. The present progressive would be "is flowing".
To give a simple rule (though as with all simple rules in English, I'm sure there will be exceptions), it's only the passive voice if there is something happening to something, but it is not stated (other than in an adverbial) who or what did that thing to it.
ADDED AFTER QUESTION EDIT:
Your example sentence, with "when he called", clarifies matters somewhat. "Was not flowed" is not, in any case, correct grammar, so should not be used. However, give the "he called", putting the whole sentence overall in the past, and the question of when it flowed (or didn't) even further in the past, the past perfect is appropriate:
"Input had not flowed into the system when he called, so I asked him to wait."