Ykhjuy

We will not [says Socrates] then allow our charges, whom we
expect to prove good men, being men, to play the parts of
women and imitate a woman young or old wrangling with
her husband, defying heaven, loudly boasting, fortunate in
her own conceit, or involved in misfortune and possessed by
grief and lamentation – still less a woman that is sick, in
love, or in labor . . . Nor may they imitate slaves, female and
male, doing the offices of slaves . . . Nor yet, as it seems, bad
men who are cowards and who do the opposite of the things
we just now spoke of [things done by men who are “brave,
sober, pious, free”], reviling and lampooning one another,
speaking foul words in their cups or when sober and in other
ways sinning against themselves and others in word and
deed after the fashion of such men. And I take it they must
not form the habit of likening themselves to madmen either
in words nor yet in deeds. For while knowledge they must
have both of mad and bad men and women, they must do
and imitate nothing of this kind . . . Are they to imitate smiths
and other craftsmen or the rowers of triremes and those
who call the time to them or other things connected
therewith?

I haven't got any idea about the meaning of "for while knowledge" this structure is new for me.

This passage is from the book named: On literature.

For while knowledge they must have both of mad and bad men and women, they must do and imitate nothing of this kind...

...is (clumsy, imho¹) resequencing and circumlocutory phrasing of the more easily understood...

For while they must have knowledge of both mad and bad men and women, they must not do or imitate anything like this...

Here "for while" could be replaced more casually with "because even though".

¹ In all fairness, I should point out that it's a translation (from almost a century ago), which may even reflect the original ancient Greek construction. But I wouldn't expect any "modern" translation to include such roundabout phrasing.

As regards the "introductory" element For while - the first point to make is that this is an entirely optional component. Within which while can be understood as meaning although...

Although they must do this, they must not do that

...equivalent to...
They must do this, but they must not do that

As a general rule of thumb I think the second version is to be preferred - to me at least, it seems easier to parse (but this is a very fine point of style).

And the initial word For is really just another somewhat outdated "stylistic flourish" (but in principle it could be understood as meaning because - referring to and explaining the preceding sentence). If you look at older versions of the Bible, for example, you'll find quite a lot of sentences that start with For for no obvious reason. It doesn't really "mean" anything at all.