The idea of a language called "Aklo" was first put forth by Arthur Machen in his short story "The White People" (1906). All that Machen tells us of Aklo is this:
I must not write down ... the way to make the Aklo letters ...
That is, Machen specifically tells us nothing.
Lovecraft, who loved Machen's story, took up the idea of a "dark language" and used it in his short stories "The Dunwich Horror" (1929) and "The Haunter of the Dark" (1936). In "The Dunwich Horror" Lovecraft tells us about Aklo:
"Today learned the Aklo for the Sabaoth," ... He that came with the Aklo Sabaoth said I may be transfigured ...
and in "The Haunter of the Dark" he tells us:
It was in June that Blake’s diary told of his victory over the cryptogram. The text was, he found, in the dark Aklo language used by certain cults of evil antiquity, and known to him in a halting way through previous researches. The diary is strangely reticent about what Blake deciphered, but he was patently awed and disconcerted by his results.
That is, Lovecraft, like Machen, tells us nothing about Aklo.
Machen and Lovecraft are the authoritative authors when it comes to the worlds they have depicted. Later authors, such as Alan Moore, have inventend additions that are not part of the canon and therefore cannot be used to learn more about the Lovecraftian universe.
Aklo is neither a constructed language nor a language system, as many sources on the internet claim, because the inventors of that language have not come up with any details beyond the name of the language. Lovecraft and Machen have not constructed a language system. All they have done is invent the name for a language that does not exist. Aklo is a fictional language, unlike Klingon or Tolkien's Elvish, which are real languages. Klingon and Elvish are constructed languages, not natural languages, but they can be spoken and written like English or French.
Ergo, there is no Aklo dictionary, because there cannot be one.