Endicia integration in Linnworks desktop should have stopped working from June 30th, but it seems that Endicia stopped supporting it only from yesterday which is why there is a problem printing.
There is a new Endicia Label Server integration available in Linnworks.net that has even more services available. Flat Rate Box packaging can be configured by mapping USPS packaging types with your Linnworks packaging types. Please see this documentation page for more information: https://www.linnworks.com/support/shipping-management/packaging-mapping
Please see support ticket you created where I described how to configure this in more details.