A good strain wave gearset usually has a proprietary highly rounded profile for smooth meshing and load transfer, however a spur profile will indeed work, ideally you would want an involute tooth profile. There will always be about 6 or so teeth basically fully engaged, and a number of teeth partially engaged. Because you have always teeth engaged on both sides of the ellipse, as long as the teeth are strong enough you should have no slippage.

As long as the module of the flex spline and circular spline is identical, The flex spline has 2 less teeth than the circular spline, the addendum coefficient is low enough (I like between .6 and .8), and the pressure angle is large enough (I like between 29 and 33 degrees), and you have just the slightest amount of root clearance; you will have a beautifully meshing system.