If a neighbor's dog barking all the time is bad, then different dogs making noise throughout the day is really bad.

I have talked to them directly and they have been very uncooperative and defiant, such as "nothin' we can do, animal clinics are loud, train tracks are loud" and "we were here before your complex".
For many years, the regulatory agencies couldn't touch them. The city told me animal noise is in the jurisdiction of the county animal dept, the county told me the animal clinic is exempt, because it's a kennel like facility.

Finally, the loop hole has been plugged and city amended its ordinance to include "animal noise from commercial facilities" into enforceable matter. Only after complaining to the city, the animal clinic reduced noise during late night/early mornings, but they continue to make disturbing noise from about 7AM to 9PM, Monday through Saturday, sometimes on Sundays.

So, when I wake up, it's their damn barking, When I get home I get an earful of barking. If I'm home one day, I hear the barking all day long. I have the windows tightly closed, but with the vent opening for treatment area being right by it, it's still disturbingly loud.

The fact their facility pre-dated our complex should not matter and a city noise officer agreed. It's just like you can make all the noise you want and not have anyone complain while the house next to yours is vacant, but it doesn't mean that if someone moves in, you can continue to make noise that would disturb them.

So, animal clinic lets dogs bark all day. They're completely uncooperative. City has ordinances but its taking them months after months and the problem is not resolved.

Any advise?

Your main complaint is with the city that granted the permit to build residential next to an existing business.

You remind me of the people who built their dream McMansion next to a farm, then complained to the highest levels of government that the farm animals were noisy and smelled like animals. They lost and moved.

The animal clinic isn't "letting" the dogs bark. They are a business which caters to and houses numerous dogs. Dogs bark. Your comparison to making noise next to a vacant house doesn't hold water, as this is not a residence, it's a business. A business that was there before you moved in, and was there before your building was even built. I say shame on you for hassling the business owner! Buy ear plugs or move.