As you likely know, Henry Hill's Aviary (Henry's Aviary) of Seguin Texas was last mapped, advertising in June and August of 1990. At that time, it listed their phone number as: 512 639 4343.
Since that time, there has been no mapped activities of Henry's. It is very possible that they have continued to operated as a small Private Business and not paid for advertising, relying on word-of-month and/or their store front, which is common with older family operations.
Since you provided no timelines as part of your Thread, i.e. how old is your Parrot and/or when you purchased your Parrot from them, it is impossible to timeline a search without guessing at it.
Best of Luck in your search efforts!