Good afternoon Everycal,
I've recently returned from a trip to CZ with my firearm and ammunition.
So with the demise of the EFP the process requires an application to the CZ embassy and depending on where you live dictates which consulate you apply, northern applications are made to Manchester.
Manchester.Consulate@mzv.gov.cz
Those further south, it will be London.
A scan of the following is required to support the permit application
1) Passport
2) Firearms Certificate
3) Official Invitation
4) Flight details, booking confirmation
5) Completed application form, link below
All of this information is submitted online and once the application is processed you will pick up the permit from the consulate dealing with the application.
When you attend the consulate to pick up the permit you need to pay for the permit.
If at all possible, and depending on who you will be flying with, I would also suggest collecting the form(s) the operator uses to check-in your firearm(s) and ammunition. By way of example with Easyjet this is one form with four pages so carbon copies are generated (3) from the original; they use these to track your kit through the system ensuring a chain of custody. My approach is to have these completed and as much pre-prepared prior to arriving at the check-in desk to hopefully reduce the the possibility of any delay.
Hope this helps.