Translation:My younger brother and younger sister have three fishes.
It would be "fish" if all are of the same species, otherwise "fishes". Given the lack of context, both should be acceptable.
Fish is the usual plural. Btw, "loaves and fishes" does not indicate multiple species.
By the way native english speakers talk it should but my guess would be that vietnamese is much more clear about the age relationship so they want to stress that.
It's fine to accept "three fishes" but since very few people say it that way any more it should not be the default answer.
Read your reference again. "Fishes" has few modern uses and the one cited is in the field of biology. In normal conversation this use is not normally observed.
"There is a boy here that hath five barley loaves and two FISHES" (Published in 1589)
"There is a boy here who has five barley loaves and two FISH." (Published in 2011)