newer android versions hide the setting to do it but it is usually still there.
go to the settings app, then wifi, then look for the drop down menu. it'll have "advanced wifi" setting somewhere in there. from there you can find the wifi direct/mirroring settings to turn on. once turned on, it should find and list your amazon stick to connect to. i do find that mirroring introduces a noticeable audio lag when playing media of any type. so be sure your player of choice has the option to adjust audio timing to compensate. my phone i use for this has a 250 ms delay i have to adjust for. yours will vary. good luck