"Of" is the correct preposition in this case, due to idiomatic usage of the phrase "speaking ill".
"Speaking of" someone or something means to mention them. "Speaking ill of" someone means to mention something bad about them. "Speaking on" X means that X is either a topic of conversation or that X is a platform on which one speaks (e.g. Skype, speakerphone, a stage, etc.).
Alternatively, if I were to make negative things about a person the topic of a speech or conversation, I could say "speaking on the topic of [insert negative things here]", or simply use "speaking ill" as a short hand.
Source: I am a native NA English speaker.