chain(x) is a shortcut for chain.from_iterable(iter(x)).

Neither copy.copy() nor __reduce__ don't have particular relation to this. Consider following example:

>>> from itertools import chain
>>> i = iter([[1, 2, 3], [4, 5, 6]])
>>> a = chain.from_iterable(i)
>>> b = chain.from_iterable(i)
>>> next(a)
1
>>> next(b)
4
>>> tuple(a)
(2, 3)
>>> tuple(b)
(5, 6)