Hi. I am not aware of any research that undermines the use of multiple approaches to teaching content in a single lesson. On the contrary, I think most people would agree that this is good practice, giving pupils more hooks onto which to hang their learning. By contrast, problems with Learning Styles include the assumption that (a) individuals can only learn well in one way; (b) all content can be taught equally well via all modalities (i.e. Visual, Auditory or Kinaesthetic); and (c) individuals need to be taught in the same way for all subjects. None of this has been found to be true and taking a Learning Styles approach has not been found to predict enhanced progress or achievement. You might find this paper interesting:
Willingham, D. T., Hughes, E. M., & Dobolyi, D. G. (2015). The scientific status of learning styles theories. Teaching of Psychology, 42(3), 266-271.