What constitutes a legal conflict of interest?

It may be a conflict of interest in the common sense meaning of the word, but that does not mean there is anything illegal about it. People may generally invest in more than one company, even if those companies compete, have conflicting interests, or one is trying to buy the other; similarly, an investor could want you to sell to him directly, to do business with him or a company he owns, etc. Unless he signed an agreement stating that he would not pursue deals that pose a conflict with your company, he is free to do; merely investing in a company does not make someone a fiduciary.

However, if he is using for his own benefit proprietary information about your company that he only had access to because of his relationship, he *might* be doing something improper there, but again, probably only if he'd signed some sort of agreement to keep information confidential or not use it for his own benefit or the benefit of third parties.