The keeping of chickens is allowed in A-1 (Agriculture) zoning in the unincorporated areas of Jefferson County. The property at 1612 Glenridge Drive is zoned A-1, and will allow for keeping of chickens.
The Zoning Regulations require large setbacks for commercial chicken houses. Such structures would have to be located 300 feet from any road right of way and any other residence. They would also have to be located 100 feet from any property line. Given the size of the property at 1612 Glenridge Drive, there doesn't appear to be adequate space to construct a commercial chicken house. Any chickens kept on the property would have to be for personal use (and not for commercial purposes).
There are no restrictions regarding the number of chickens that could be kept on the property. There could be applicable health codes that could apply, but those would be enforced by the Jefferson County Department of Health. You may want to contact them to inquire about possible requirements from a health code/public nuisance standpoint. Their number is 205-933-9110, and here's a link to their "contact us" web portal: https://jcdh.org/SitePages/ContactUs/ContactUs.aspx
Please let me know if you have any additional questions.
Michael R. Morrison - Zoning Administrator
Jefferson County Department of Development Services
Room B-200, Courthouse Annex
716 Richard Arrington, Jr. Blvd. N
Birmingham, AL 35203