That is an intriguing question and I believe that what WisdomBeing have mentioned is a normal method from which a being can take rebirth by the force of karma. Cloning have perhaps created a new method for beings to take rebirth. The attraction to the male and female organs is just a method but the real cause behind that is karma. So I think cloning have created new circumstances for beings to take rebirth under the same controlling factor, which is karma. Well, that is how I would see it.
Logically speaking, clones should also have different mindstreams. The union of the female and male should not always be required. After all, there are beings born from heat, and also those born in the formless realms. In these cases, there should not be any union occuring...
I agree with Thor as I too believe there are different ways of taking rebirth. The one we speak of with regards to the union of male and female is but one method of "creation" and as such, one method of rebirth. As mentioned again by Thor there are those beings born from heat, those born in the formless realms whereby no conventional union (as we perceive) is needed.
So with that logic, cloning could result in a similar fruition... in that a mindstream could be attracted to the conditions whereby it could attach itself to a host much like born of conventional union. I do not believe for one moment our mind streams would say "hey, it is not from conventional union, I will not go there!".
If it is a fully functional animal so why not. After all, if we did take rebirth as an animal, clone or otherwise it is the our very karma that decides that. I do not think there is a distinction hence my answer would mimic that of Thor in that cloned animals would have different mindstreams.