Right away there's too much information. It's a big block of text that we don't need, get rid of the unnecessary words...
I am selling a 10 year old Egyptian Arabian mare by the name of Flame. She is registered under the name of CG Shalimaars Flame, and I do have the papers, they just have to be transferred over.
She's registered, you don't need to say that you have the papers and they've been transferred over. I also prefer to see the basic info (name, age, breed, registered status, gender, etc.) listed so you can take a look, see if it's what you're interested in and THEN read on about temperament, etc.
She does have minor arthritis in her hocks, and 2 nasty scars on her legs from a run in with steel. The scars do not affect her in any way.
I would mention the arthritis, but not the scars. If they REALLY don't affect her there's no reason to mention them in the initial ad, they can come up later in conversation.
Flame was owned by a man with a short temper, so if she is smacked, even if it's light, she does get scared. What she needs is a patient owner that will go at her speed, not theirs.
Was she actually abused? Aka beaten / neglected? If not, I don't think it's something you need to mention in the ad. Again, it can come up later when you're talking about her 'vices' ie: she responds better to verbal reprimands than physical. The way it's worded sounds like an excuse.
She is good with the farrier and vet, being clipped, groomed, tied, and stalled. She does need work on bathing.
List what she's good at, people will ask you how well she bathes and then you can tell them. You don't need to include all her faults in the ad.
he is up to date on shots, but does not have a coggins as of now.
You might want to get that coggins, or be prepared to take $$$ off the sales price.
Flame also could use her teeth done before being ridden in a bridle (I've been riding her in a halter).
Same here, and I wouldn't say it in the ad, it'll turn more people off than you'll have interested.