NNF....a little Proxxon FKSE table saw with the TCT blade would complete your task without issue....perfect squareness & straightness of the sawn product

6.35 plank width + 1.6 blade kerf = 7.96

...so each slat would provide 3 x planks

...
Your material nomination of walnut is interesting

.....the specie of walnut material [hard, tough, beautifully and contextually grained and many hundreds of years in age] and are commonly used for surface laminates ......... Derek
Courtesy of the WIKI people.......
Walnut shoot cut longitudinally to show chambered pith, scale in mm
The common walnut and the black walnut and its allies, are important for their attractive timber, which is hard, dense, tight-grained and polishes to a very smooth finish. The colour ranges from creamy white in the sapwood to a dark chocolate colour in the heartwood. When kiln-dried, walnut wood tends toward a dull brown colour, but when air-dried can become a rich purplish-brown. Because of its colour, hardness and grain, it is a prized furniture and carving wood. Walnut burls (or 'burrs' in Europe) are commonly used to create bowls and other turned pieces.