As far as I can see, testing the existence of the kiki/bouba effect in primates is technically impossible, because of their lack of speech and/or potential bias due to training effects inherently necessary for animal behavioral experiments.
The reasoning in that other question was basically as follows:
Cats [read: non-human animals] don't have that kind of repertoire of phonemes. So regardless the > similarity in some brain areas [of animals other than modern day humans], I dare to say a bouba/kiki or
baluba/takete effect can never be found in cats [or any other non-human animals].
Hence - along those lines the answer to your question is 'no', as the bouba/kiki effect can simply not be tested in its current form in non-human animals, because the latter are not capable of uttering the words bouba or kiki. An interesting note on this are parrots and related species that are capable of reproducing human speech. However, they simply imitate the sounds, just like other species of birds imitate the sounds of ringtones and the likes. That, however, does not mean they associate those words or sounds with the meaning they have to us.
Further, as suggested in that previous answer; synesthesia and cross-modal associations can certainly not be ruled out by any means.
An interesting side track on your question would be the question wether there are cross-cultural differences within the human species. For example, folks speaking languages unrelated to Western languages, like the tonal language Chinese Mandarin, may produce a different outcome in the same bouba/kiki test.
The comment from ArnonWeinberg is an interesting one - why not train an animal to point at one of the two graphs when hearing bouba or kiki? Well, the issue here is that the animal needs training; the trick with the bouba/kiki effect is that naive people assign the same pointy structure to the work kiki and the blobby image to bouba. If one would train an animal the trainer needs to reward (or punish) the animal when it responds in a satisfactory way. That means the experimenter's influence on the animal's response will be paramount for the outcome of the experiment. In turn, a trained animal will respond the way it was taught, which is not the intention of this experiment.