The Royal Style 8 belt and Kirby 301291 are both knurled belts and EXACTLY IDENTICAL in size. You can use both interchangeably on a Kirby or Royal vacuum, as long as the Kirby has a ball bearing brushroll, not the sleeve bearing silver ones used before the Generation 3 came out in 1991. If you have a older Kirby and have replaced the brushroll, you should be fine, just remove the plastic endcap to check if you have the ball bearings. On a Royal, make sure it was a model made after 1990. According to Ben Edge, KirbyClassicIII here, the Royal Style 8 and Kirby 301291 knurled belts put too much stress on the brushroll and the motor bearings on a Royal made before 1990. Both Royal and Kirby make genuine belts with softer rubber for the older models, if Ben Edge reads this he can give part numbers for both.
As Lesinutah said above, the Eureka PT and AR belts are also identical in size and can be used on a Royal or Kirby too, and both the Royal Style 8 and Kirby 301291 can be used on a Eureka powerhead, DustCare PB11 powerheads that take flat belts, and Royal Lexon and Dirt Devil Power Pak powerheads, as can the Eureka belts. In fact, these powerheads were designed off the Eureka powerheads in the first place. However, a word of caution about Lesinutah's advice about using any of these belts on a Rainbow powerhead made after the D2 - DO NOT USE A NEW BELT ON THEM! The OEM Rainbow belt is the same width but slightly longer, so you will put stress on the brushroll bearings and cause them to wear prematurely. All 4 of these belts can ONLY be used new on a Rainbow D2 powerhead, as that powerhead was made for them by Eureka and is another version of the Eureka RotoMatic powerhead which many companies in the old days used. If however, you also have a Eureka, Dustcare PB11 or Royal powerhead that uses the Royal Style 8 or Kirby 301291 knurled belts, save the old belt when you change it for a new one and use it in the Rainbow powerhead - it will be stretched enough to be the correct length and width to use on a Rainbow powerhead without stressing the brushroll bearings. Also, if you like, look up generic Kirby powerhead belts on Ebay, AliExpress and Amazon - I have used the generic knurled Kirby belts in the past with good results.