How exactly does symbolic language for apes work?
The best article I found was this one. In it it says among other things that:

Kanzi, an unusually intelligent Bonobo chimp trained at Georgia State
University, was remarkable in that he learned to use around 200
symbols on a portable electronic symbol board, a computer with buttons
in the shape of absolute arbitrary symbols rather than manual signs.
More interestingly, Kanzi learned how to use this board while watching
his foster mother, Matata, being taught by traditional reinforcement
methods. So Kanzi did learn how to use arbitrary symbols without being
taught, although he did observe direct reinforcement of each symbol
during the process and the symbols were taught one at the time.
The
evidence for the mastery of syntax is not so convincing. While
chimpanzees can learn to order their symbols to get what they want, it
is not clear that they have mastered syntax. The reason is that when
they initiate communication, even adult chimps often abandon the order
they have learned and phrases such as, &quot;Fight mad Austin,&quot; a famous
utterance of Kanzi's friend Panbinisha. Here the order doesn't seem to
matter. Apparently Panbinisha was trying to express, &quot;there was a
fight at Austin's and someone (Austin?) was mad&quot;. It is interesting
that even human children simply don't make such errors once language
acquisition begins, and certainly adult speakers would never utter
such strings. Notice it lacks any morphemes (-ing, at, I, she, -ed),
the hallmarks of grammar.

The trainer of Kanzi has published some materials but I do not know if they are available free online. You could probably send her an email and ask. The article goes on to state:

The maximum number of lexeme symbols (simple nouns, verbs, and
adjectives) is interesting, too. The brightest chimpanzees master
fewer than 200 of these symbols by adulthood. Human children know
about 50 by the time they are 18 months old, when they begin learning
nouns, verbs, and adjectives at the rate of about 5 per day. So the
maximum achievement in symbol acquisition among other primates is more
than matched by human children before the onset of language
acquisition. In fact, the type of phrases spoken by chimpanzees and
gorillas also resemble those spoken by children before they acquire
their first language: &quot;give orange&quot; or &quot;give Bobby orange&quot; (without
the pronoun me) are common expressions of children before the onset of
language learning around the age of two.
The results suggest that
while chimpanzees and gorillas are far more intelligent than anyone
had imagined during the first half of this century, they are not
capable of human language. Rather, they have a primitive version of
the semantic ability children use before that explosion of
language-learning around the age of two.

At least according to that article there is not much of a grammatical structure at all. The apes does not so much care about the order of the words either, even if the can learn a certain order, especially if they get something to eat if they do it right.