Don't know what actual drug is in Miracle Life, but if it's a cocci treatment theres no reason why it would conflict with Amoxycillin being given also.
Are the birds actually suffering from an illness that requires an antibiotic like amoxycillin? I ask because routine dosing with antibiotics is not recommended, due to the problem of bacteria developing resistance.
I was reading about this today for one of my rescues, and amoxicillin should not be mixed with Sulfa antibiotics apparently. It deteriorates the action of the amoxicillin, in the way adding tetracyclines to amoxicillin does. The tests I read were on chickens.
One way to deal with the coccidia whilst having your birds on Amoxicillin is to treat with amprolium, which i have done myself several times now. I would suggest giving the amprolium in between doses with amoxicillin as it can occasionally cause regurgitation in my experiences with it. Its about the best medicine to treat coccidia though.