Because platinum oxidizes only very slowly, Pt points (actually, Pt alloyed with Ir, Ru, and/or Os) were used in the earliest magnetos before it was realized laminated armatures significantly improved the low speed operation for which it had been felt Pt provided an advantage. Perhaps because of this, and citing a "lower surface resistance," shop manuals often say Pt should be used for the contacts in magnetos intended for higher performance motorcycles. However, despite what is commonly written, my measurements show that the difference in surface resistance between the two metals is negligible unless the magneto sits unused for many months in a humid garage, in which case tungsten can benefit from a light burnishing to remove the resistive oxide.
The contact resistance of a set of points is small enough that it isn't easy to measure, but the resistance of the tungsten points in a KNC1 magneto varied between 2 and 11 mΩ when I measured it after successive make/breaks when I rotated the armature by hand. Since 10 mΩ is less than 2% of the resistance of the primary coil itself, the contact resistance of these points will only reduce the primary current, and hence the output of the magneto, by ~2%. What this means is, even if the resistance of Pt points were zero (which it isn't), the output of two otherwise identical magnetos with Pt and W points in good condition would differ by a negligible amount.
If you still want to use Pt points, well, just because you want to, although Pt will resist oxidation in a humid environment better than W, it reacts with organic vapors to form PtC, which is both resistive and rapidly erodes the contacts. The choice of materials for magneto points is addressed in Chapter V 'The Magneto-Type Ignition Systems' of Electrical Contacts Data Book: Materials, Designs, and Applications (P.R. Mallory & Co., 1945): "… because of the location of the magneto and its design, the contacts may be subjected to oil mist. In such cases it has been the practice to use tungsten for the contacts, because platinum and its alloys have a tendency to become brittle… [causing] high contact resistance and a corresponding high rate of electrical erosion."
If no replacement points are readily available the old ones can be refurbished by silver soldering short lengths of pure tungsten TIG electrode rod over the ends of the worn points (Pt can be soldered as well, if you if you insist on using it). Tungsten wets easily with silver solders, and a single 7" piece of 4 mm-dia. pure tungsten rod is enough to restore a lifetime's worth of magnetos. If you decide to try this, you need to use pure tungsten TIG electrodes, which are painted green on one end. Do not use rods with either red or yellow ends because they contain 1–2% radioactive thorium. Because of the nature of the radioactivity, in solid form this isn't an issue, but you don't want to breathe the dust created when you cut it with an abrasive wheel and have it permanently settle on the surface of your lungs. Also, the reason for thorium is that it makes it easier for the TIG electrode to emit electrons, and that is the opposite of what you want in contact breaker points. When the points separate, you would like it to be as difficult as possible for an arc to form.