Well, that, here, is the problem with copying and pasting random snippets from the internet without understanding what they do: they are little black boxes that one can't modify or extend at will by lack of knowledge.
Let's deconstruct the first mapping:
vnoremap J :m '>+1<CR>gv=gv
:[range]m {address} moves the lines covered by [range] to below line {address}. Here, the range is automatically injected by Vim: '<,'> which means "from the first line of the latest visual selection to its last line", and the address is '>+1, meaning "the last line of the latest visual selection + 1 line". So :'<,'>m '>+1<CR> effectively moves the selected lines below themselves,
gv reselects the latest visual selection,
= indents it,
gv reselects it again for further Js or Ks.
Now, we want a similar mapping but for copying the given lines. Maybe we can start with :help :m and scroll around?
Sure enough we find :help :copy right above :help :move, which we can try right away:
xnoremap <key> :co '>+1<CR>gv=gv
Hmm, it doesn't really work the way we want but that was rather predictable:
- the address is one line below the last line of the selection,
- the selection is reselected and indented, which is pointless.
We can fix the first issue by removing the +1:
xnoremap <key> :co '><CR>gv=gv
and fix the second one by selecting the copied lines instead of reselecting the latest selection:
xnoremap <key> :co '><CR>V'[=gv
See :help :copy and :help '[.