Don't tap off of another duct.
If it's only 10 feet, a flex duct will work and would be easier and faster for you. If you use metal, you'll have to insulate it and get the proper fittings.
A duct starts off of the plenum (take it from the side, unless there is no other place) with a "tor" or "starting collar" that is fixed to the plenum, then you can tape or strap the duct at the joints (special tape) and screw the joints of metal duct.
If you come off of the top of the plenum- use a damper in the start collar to adjust the air.
*Metal duct - screws and tape.
*Flex duct - Duct straps and or 181 approved tape.
The cardboard duct as you called it is ductboard made from glued compressed fiberglass with a metal foil glued on the outside.

Plan to place register boot above closet door and once in closet come into attic with conecting elbows. In attic I would like to transion from 6" connectors to 8" flex which will run the 10' to plenium.

? is... The transition collar at the 6" end is female and the 6" elbow piece is female, now what? Will the 8" transition end which also is female allow the 8" flex duct to slide over it? Also it sounds like I need to wrap all metal joints with insulation in attic and in closet, once wrapped what keeps insulation in place, duct tape? Can I use any sheet metal screw for connectors? Was suggested to place damper at plenium because told it would keep down on noise. The most expensive duct tape at Home Depot found in duct area was Scotch Duct Heavy Duty All Weather meets UL-723...sound ok or where do I buy somethng else?

Sincerely appreciate your input.

I like the metal duct tape. There is a paper tape with metalized backing that works almost as well. The surface needs to be clean and dry before using the tape. Both are normally available at HD. If the round duct is not self locking, It is not legal to use screws. Tape it good, insulate it, then seal with tape. Use mastic for all joints. I would also recommend using spray foam on top of the insulation as a higher insulative value.

How do I join to pieces that both are female? Do They make a piece that is male to male? Could not find at HD or Lowes.