They do and I've used the device. The provide a black mounted box that sits in the cup holder and hangs out about eye level. Not as good as captioning glasses, but gets the job done
I've never heard or seen anything like this at the AMC. Maybe if your in the area you can physically ask an employee. You probably won't have any luck tracking down a manager.
I believe they do provide devices to assist in amplifying audio and providing closed captioning. You'll need to inquire about the devices at their service counter. Look on amc.com and the showtimes will have (cc) next to it if offered. I'm sorry they're not answering!
I've been to a lot of movies here, 100+, and have never seen closed captions. I know that's not a definitive answer but I don't think they do.
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