Do beings have control where they get re-incarnated

It is possible, however it is off chance.
How about that off chance possible?
The reincarnator must does:

1. Much enough merit.
   Because the merits cause the rebirth in a new good life, such as a human life, angel.
   See: K.N.Dhammapada's Commentary Patipūjikā, and chaddanta-jātaka's commentary.
2. Very strong efforts of mind's desire, intention, management, inspiration, decision, etc, to act about "specified new life" in every life's moments, until he die.
   Because the strong efforts to keep regularly actions that cause of target new life, will send you to be the specified new life, as a director. It is like a transgender man who use every second of life to act like a woman.
   See: A.N. Sattakanipāta Saṃyogasuttaṃ.
3. Die just in the same millisecond of new life fertilization.
   Because the dead-mind is immediate contiguity cause of rebirth-mind. And mind arising and vanishing is very fast (over trillions times per snap finger).
   See: Sanṅgaha 4th chapter.

However it is still very hard, so buddha taught in Pansu Suttas:

"The great earth is far greater, lord. The little bit of dust the Blessed One has picked up with the tip of his fingernail is next to nothing. It doesn't even count. It's no comparison. It's not even a fraction, this little bit of dust the Blessed One has picked up with the tip of his fingernail, when compared with the great earth.
"In the same way, monks, few are the beings who, on passing away from the human realm, are reborn among human beings. Far more are the beings who, on passing away from the human realm, are reborn in the animal womb... in the domain of the hungry ghosts.

You can see that it is very very hard to success. And all the way, you still will be old and dead after that. So, theravāda buddhism never support whole rebirth and reincarnation. We have jātaka, rebirth cannon, just for an inspiration and faith in buddha's ability and experience.

Nowhere you can avoid the suffering, if you still rebirth

This image captured from TEACHING & TRAINING book of Pa-auk monastery: