I've lived over 30 years in Kansas, in both ends of the state. I haven't toured straight through the Great Plains, but I've ridden many touring-distance days in every direction on the plains. I ride every day, so I think about and experience the wind out here as a matter of course. When I do ride the plains straight across, wind won't factor into which direction I go. While you may get more west wind days than east, you're at least as likely to get several days of sustained 20+ mph winds from the south. Or it might be still for a day or two. You can be sure you're going to get real wind more often than not in late spring/early summer, but from where, for how long, and much of it no one can tell you. Riding as early in the day as possible will help as the wind usually dies down at night.

Maybe it's more predictable as you approach the front range, but here in the middle it's hard to say, and no one's week-long trip experience is going to help predict what it will be when you're here. I'll attest that hours of a 20 mph headwind day after day can be discouraging, but as far as planning goes, historical weather data will be as helpful as anything else.

In any case, the plains make for beautiful riding.