
Welcome to the forum. glad you joined!
By your question I assume you are somewhere north of the equator. That helps some with my response. If you are going to stick around it can help if you modify your profile to show your general location. That can help on a lot of different questions, not just about climate questions.
Part of which is better for you may depend a bit on why you want chicks. What are your goals? Why do you want chickens? That might possibly make a difference but I'll assume you want eggs and/or pets.
I think the pros greatly outweigh the cons. I may think of a con while I'm typing this. The weather is going to be really good in august, though possibly really hot. Depending on your weather you won't have to provide heat for very long and can probably get them outside really young. If yo are brooding them in your house you may fine that you want them out as soon as you can due to the dust, noise, and possible smell.
If you get them in August you should get eggs really early in the spring instead of waiting until next fall.
You are getting them from a feed store so you don;t have to worry about shipping them in extreme cold or extreme hot. That's a wash.
Your coop needs to be ready when you get them. They grow awfully fast and life can get in the way of construction schedules. Get busy. Now!
I just don't see any downsides to getting them in August.