I can't edit chat messages as in the instruction menu (using the new interface; looks a little out-of-CSS but that's cool). I think they are not available. I know that Message response options symbols intermittently not loaded on mobile chat exists but its case is the buttons are loading half the time and only flag button is visible in that half time, where in my question there is no edit button or flag button viewable anytime.
I don't know the reputation requirements or if there is one.