Without having checked in too much detail (your commands posted do not appear to be exactly what you ran: mrtransport should be mrtransform, flirt does not work with .mif images), I’d suspect the transformation worked but mrview shows you the rotated image.
Do the images look aligned when one is shown as an overlay? mrview mean_dwiAP_den_unr_preproc_b0.mif -overlay.load r_dwiPA_den_unr_preproc.mif -overlay.opacity 0.3 If so, everything is aligned in scanner space. Note, you can but don’t need to resample one image onto the grid of the other via mrtransform 's-template` option.
If the overlay is not aligned with the main image, please check that the transformed moving image produced by flirt is aligned with the target image and double-check that the commands including and after the flirt call are what you ran and we’ll have another look.