It sounds like higher register/elevated writing to me. I don’t believe it is wrong, but if it doesn’t match the tone of the rest of the writing then it will sound stilted.
Did a quick Google search using some terms using that same pattern and got some results:
13 results for “avail your company of”
565 results for “avail you of”
3 results for “avails the company of”
Considering the register of the phrase, it’s not surprising to find fewer occurences of it on this sort of search. And most of the hits come in fairly well-worded texts (at least, from a cursory inspection). So, despite not having many hits, it looks like the phrase is correct.
But again, if the rest of the text doesn’t use the same register, then you can safely get rid of it.