where it is a flat rate box, I wouldn't use USPS Rate lookup, it is waisted trip to to the USPS servers.
just create a shipping rule that if the weifght is above 13oz, use the flat rate charge.
according to the USPS site:
https://store.usps.com/store/browse/uspsProductDetailMultiSkuDropDown.jsp?categoryNavIds=catGetMailingShippingSupplies%3asubcatMSS_PriorityMail&categoryNav=false&navAction=push&navCount=0&productId=P_O_FRB1&categoryId=subcatMSS_PriorityMail
The Domestic Priority Mail rate would be $12.35
so create a flat rate shipping rule for 13.35 above 13 ounces