Chick with constant messy bottom

How long has she been doing this, when did it start? Have you moved them inside/outside or changed feed or anything in that time frame? I would consider stopping the AVC for awhile, and maybe changing feed to see if it is just something that she doesn't tolerate as well as the others. With her age, another consideration would be a mild case of coccidia.

 

In younger chicks 'pasty butt' is often the result of the chick having a hard time with temperature control. If I add an extra light to the brooder (or bring her in to put her under a heat light if she's been outside with broody mom) it generally resolves the issue. However, in your case it seems more likely that when she poo's she squats VERY low and then then instead of the poo sticking to the shavings and her walking away its sticking to her feathers. I've had this in the Japanese bantams because they have REALLY short legs. In this case I would suggest a little oil (NOT much as you don't want to have the other chicks picking at her) such as coconut, vegetable, or bag balm that would cause the poo to slide off and will make it much easier to clean off any that does happen to stick. Rub it in as well as you can and it should help hope this was helpful in some way... and coccidia causes blood in the poo. That can be fixed with medicated feed and a very clean coop/ waterer unless its serious. however, it's unlikely as it sounds like only one of your chicks is having problems.