I used Nashua tape after watching a video on youtube. I think its 324 A aluminium foil tape, duct cleaning guys used that our house and recommended that as well.
Here is a link of video.
Yes splitting an 8” duct to 2 separate 6” ducts is an appropriate size transition, since it is a master the air will be going to the same areas while the bathroom door is open. I usually add dampers to all my vents it costs more but makes balancing easier.