I am designing a flyer for the screen and the client insists the logo should be 71mm exactly. Does the resolution plays any role on the viewer, some may see it bigger, some smaller? Thank you.
Millimeters, inches, centimeters, picas.. all do not translate universally to pixel sizes.
Pixels are not a physical object, there’s no measured size for a pixel.
Physical measurements only relate to printed materials, never anything on screen.
You need to ask your client if a pixel size is acceptable. Perhaps show him/her what 71mm would be at 72ppi (201px), 150ppi (419px), 300ppi (840px), because it will be different based upon the resolution of the image.