This is detailed in the chapter B07 of the FIDE Handbook and here is the application process as extracted from the section 6. FIDE Endorsed Academies and which reads as follows:

6.6.    Application

a)      A FIDE Endorsed Academy must be a legal entity and underwritten by a FIDE licensed trainer and must be supported by the respective National Chess Federation and/or Continental or FIDE Affiliated Organization in its jurisdiction, with a 10 working days period for any objections. In exceptional cases, however, TRG may accept other written confirmations of the applicant’s good reputation, provided that such confirmations are exhaustive, reliable and confirm the reputation without any reasonable doubt.

b)      An application must be made together with the registration fee which is inclusive of the year of award.

c)      It is a requirement that a FIDE Endorsed Academy has FIDE licensed trainers in its employment.

d)      FIDE Endorsed Academies shall be named appropriately. An academy shall not be seen to represent a country or federation – without being owned or run exclusively by that federation. Nor shall the Academy be named in a way that can mislead third parties – for example by being seen as a part of FIDE, rather than affiliated with FIDE.