Despite the adherence by many school systems and informal learning institutions to Howard Gardner's theory of multiple intelligences, first proposed in 1983 in his "Frames of Mind: The Theory of Multiple Intelligences," there is as yet no neurological evidence for the existence of multiple intelligences nor the effectiveness of "teaching to the learning style." One comprehensive critique of the theory came from Lynn Waterhouse in a paper for Educational Psychologist (2006: 41(4), 247–255) entitled, "Multiple Intelligences, the Mozart Effect, and Emotional Intelligence: A Critical Review." Dozens of others have been published noting the same lack of evidence for the theory, despite almost three decades of growing application of the theory to educational practices. Dr. Patrick Groff at the National Right to Read Foundation addressed your specific question in a brief paper, which includes references to other critiques:
Gardner himself has refused to define what he really means by "intelligence" beyond attempting to broaden our understanding of intelligence beyond IQ scoring. He has also acknowledged that there is no way to test who has what ability; he called any attempt at classification "an artistic judgment." Given that, it would seem impossible to properly classify any learner and then custom-build a learning program just for that person. Even if one could, there is no existing neurological evidence that doing so would result in a measurable benefit.
Gardner does include visual, kinesthetic and auditory (musical) as part of his larger classification system, but perhaps you're referring to the more specific VAK/VARK learning methodology put forward by various people in multiple variations of neurolinguistic learning models. Most of these models developed in the mid-1970s and early 1980s, contiguous with Gardner's work, although Fleming's VARK version of the original VAK comes as late as the 1990s.
Those models seem to be equally unproven based on reviews of evidence and testing methodologies by non-interested parties, notably the large 2009 review done by the Association for Psychological Science and Psychological Science in the Public Interest. The conclusion was that most testing was inadequate, seriously flawed or simply missing and that justifications for belief in the efficacy of these classifications and programs was weak at best. The study did suggest a straightforward testing methodology to prove the worth of tailored learning strategies that only a few researchers had performed; in all but one case, the findings were negative for improved educational impact. So far, at least, evidence is lacking.