Wood Grain concerns for project

Good evening, I happen to have a fair amount of 1 1/4 inch thick walnut that is shop acclimated and approximately 40 years old. I have used it for other small shop projects like picture frames etc however now i would like to attempt a more involved project. My plan is to make a shaker high chair that also can be used as a desk and rocking horse. The plans are fairly straight forward requiring glue,self tapping screws and only one dado joint in the whole project. It will require me to glue up 3 boards to make the side panels.My concern is that these boards are all flat sawn . Given that i will not be doing any cabinet type work will these boards be ok for this project? Concerned about flatness with the sides.Made a beautiful small table recently in which the top cupped fortunately before i put it together. Made the top later with quarter sawn boards which worked out well.Am i over thinking this one or should these flat sawn boards be just fine?