Not sure how the Kindle Touch or Fire work, but iBooks and the Kindle app on iPad both have tap once to flip to the previous/next page (swiping is not required).
Kindle app on Android phones also uses single tap to page; it's extremely convenient (compared to the old Kindle with physical buttons which I also use). Touch for paging is certainly no worse than the old buttons, and--really--the keyboard and cursor control on the old Kindle are just about useless. ("Up, up, up, left, down, down, up, ..." is hard to take after having a touch device.)