I know that it is a general rule that animals on flags face left. For Charleston, South Carolina, I have made a couple of designs (two depicting Charles II and one depicting Athena) where I have struggled with this rule, though. What would your advice be as to which direction Charles and Athena should be facing? And, if you should feel that this is not within your area of expertise, whom would you think I should ask?
Firstly, there's no real "rules" of flag design; breaking them doesn't necessarily make a flag "bad". I don't think I'd have noticed which way the portraits on the Charleston flags face if I had seen the page before this message.
I can't find a definitive origin of the habit of having animals and people face the hoist (the side attached to the flagpole), but a practical reason for it that I've read several times is that it makes the animal face forward if the flag is being carried by a person. It is also in accordance with heraldic tradition, as beasts on coats of arms face dexter by default (the shield bearer's right, i.e. the viewer's left).
It's up to you which way to go with it, though. I personally default to animals facing the hoist, but only noticed a week or so ago that my Missouri proposals had the bear facing right. (I'm not sure why the Missouri seal, which I copied it from, has it that way; it might be related to the German heraldic method of flipping the left half of combined coats of arms so animals face the center.)
As for where to ask things, this wiki has a forum for questions and discussion not aimed at a particular user, although I'm not sure if any other active users check it. I tend to recommend the vexillology subreddit (or its Discord) as a more responsive forum for general flag questions.