The only one burner Weber gas grill that uses Flavorizer bars is the Weber Go-Anywhere.
Sometimes you can find this on Amazon but not always. If it is available on Amazon it will be at this link.
If the Amazon vendor is out of stock you can order this directly from Weber.
The Flavorizer bar for this grill is unique and historically interesting. The whole concept of the Weber Flavorizer bar originated from this tiny grill. Weber engineers were looking for a heat distribution medium that was better than lava rock and tried installing a bent metal panel over the burner. It turned out that not only was heat distribution improved but flare ups were greatly reduced because dripping grease would vaporize on the hot metal instead of catching fire. The vaporized fat created a very flavorful smoke which resulted in this device being called a Flavorizer bar.
The Weber Flavorizer bars found on the larger Weber gas grills all originated from the heat distribution research performed on the Weber Go Anywhere. If you would like to learn more about this grilling innovation then the original Weber patent for Flavorizer bars can be read here (US Patent 4,627,408 Vaporizing element for portable grill, Dec 9, 1986; Erich J Schlosser). US4627408