I'm not sure which specific pattern you're looking for but try "encaustic tile," "star and cross" or "star and rosette."
Komodo Kamado works directly with a specific factory for their tiles, so you won't find the exact same thing off the shelf but there are plenty of companies making similar encaustic-style porcelain tiles.
Home Depot and Lowe's both carry some options, and searching for the keywords I suggested would also give you a ton of different vendors.
You might not find a perfect clone, but you can definitely get a similar look and feel without paying custom prices, especially since you're on a budget.
Just also make sure whatever you choose is rated for outdoor use and frost resistance for your fire pit project!