What is it called when two people (usually kids) stop talking for a while after a fight or an argument because they are mad at each other?
As zondo says, above, such people aren't speaking to each other. (This is pretty much true even if they do literally say a few words for logistical reasons -- "I need to get out. Move your car" -- as long as they are doing what they can to avoid speaking.)
People aren't on speaking terms if they are doing this as a sort of policy long-term. You wouldn't say that if they're just too angry to speak for a couple of days, but you would if months go by and they are deliberately avoiding speaking.
The silent treatment is a deliberate plan to punish the other party by being silent, as opposed to avoiding speaking for some other reason (like being too angry or hurt to converse).
Such people may also be avoiding each other, but that doesn't imply anger.
This sounds like a classic case of the silent treatment.
Silent treatment (often referred to as the silent treatment) is verbal silence imposed onto another. It may range from just sulking to malevolent abusive controlling behaviour. It may be a passive-aggressive form of emotional abuse in which displeasure, disapproval and contempt is exhibited through nonverbal gestures while maintaining verbal silence. Clinical psychologist Harriet Braiker identifies it as a form of manipulative punishment.
This could be used to refer to either one person not talking to another, or with two people they'd be giving each other the silent treatment, but zondo's comment of "not on speaking terms" is also valid.
For two kids, you can say they are sulking. Sulk, defined by Merriam Webster
to be angry or upset about something and to refuse to discuss it with other people
You might consider, fall out
To break a relationship or form a negative relationship as a result of a dispute.
fall out with someone; have a falling-out with someone
To break a relationship or form a negative relationship with someone.
If the mutual silence is due to an impasse in an argument, the silence can be referred to as a standoff:
An argument, contest, etc., in which there is no winner
In this case, there is no "winner" because there is no resolution.
This is related to the personality descriptor standoffish: such a person is inclined to reserved or silent disagreement rather than pursuit of a resolution or compromise.
Since the context is "usually kids", you can say that they are snubbing each other.
Snub verb 1 Rebuff, ignore, or spurn disdainfully: he snubbed faculty members and students alike - ODO