
flach
flat
Having little height or depth; level and without significant elevations or depressions.
Die Landschaft hier im Norden ist sehr flach.
The landscape here in the north is very flat.
flat / shallow
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flat
Having little height or depth; level and without significant elevations or depressions.
Die Landschaft hier im Norden ist sehr flach.
The landscape here in the north is very flat.

shallow
In a figurative sense, intellectually undemanding, superficial, or lacking depth.
Ich fand den Film langweilig, die Witze waren einfach nur flach.
I found the film boring; the jokes were just shallow.

shallow
Refers to containers or bodies of water and means that they are not deep.
Für die Suppe brauchst du einen tiefen Teller, keinen flachen.
For the soup you need a deep plate, not a shallow one.

shallow
Describes breathing that is not deep, but only superficial.
Nach dem schnellen Rennen war seine Atmung sehr schnell und flach.
After the fast race, his breathing was very quick and shallow.

to keep a low profile
To behave inconspicuously in order not to attract attention or to avoid trouble.
Nach dem Streit mit dem Chef ist es besser, wenn du dich erst mal flach hältst.
After the argument with the boss, it's better if you keep a low profile for now.
The adjective 'flach' (flat/shallow) is closely related to the noun 'die Fläche' (surface/area). A 'Fläche' is a level surface. This connection helps you understand the basic meaning of 'flach' as 'level' or 'without height.'
Der Tisch hat eine große, glatte Fläche.
The table has a large, smooth surface.
The literal meaning of 'flach' (flat/shallow) describes physical properties such as a landscape or a plate. The figurative meaning describes abstract things like jokes or conversations that lack depth or sophistication.
Das Ufer des Sees ist hier sehr flach.
The shore of the lake is very shallow here.
In its literal meaning, 'flach' (flat/shallow) can describe both low height, e.g. 'flache Landschaft' (flat landscape), and shallow depth, e.g. 'flaches Wasser' (shallow water). In both cases, it is about a small vertical extent.
Kinder können sicher im flachen Wasser spielen.
Children can play safely in shallow water.
In its figurative meaning, 'flach' (shallow) is very often used for things that are intellectually undemanding. Common combinations are 'ein flacher Witz' (a shallow joke), 'flacher Humor' (shallow humor), or 'eine flache Unterhaltung' (a shallow conversation).
Er macht ständig nur flache Witze, über die niemand lacht.
He constantly makes only shallow jokes that no one laughs at.
In a medical or sports context, 'flach' (shallow) describes breathing that is not deep. People say 'flach atmen' (to breathe shallowly) or 'eine flache Atmung' (shallow breathing).
Nach dem Sprint atmete sie sehr schnell und flach.
After the sprint, she breathed very quickly and shallowly.
The idiom 'sich flach halten' (to keep a low profile) is reflexive and means behaving inconspicuously in order to avoid attention or trouble. You deliberately withdraw.
Nach dem Fehler im Meeting sollte er sich erst einmal flach halten.
After the mistake in the meeting, he should keep a low profile for a while.
just / exactly
When referring to shapes, eben would describe a level surface without raised areas, but this meaning of eben is not included in the input. Flach explicitly describes little height or depth and can also indicate the absence of significant raised areas. For a low-profile shape, flach is therefore the attested choice.

Die Bauanleitung verlangt für den Tisch eine flache Platte mit geringer Höhe.
The instructions require a flat tabletop with little height.
Die Bauanleitung verlangt für den Tisch eine vollständig ebene Fläche.
The instructions require a completely level surface for the table.