Kenny,
With kidney stones, one episode is not a show stopper if you have normal lab studies related to kidney function and you have no retained stones. If someone has a history of a single stone, they will need to demonstrate normal labs and at least an x-ray to prove they have no further stones. An x-ray may be your preference as it will only show stones of clinical significance, whereas a CT will show even minute particles of calcification in the kidneys which will still be called "stones".
If you have more than one episode or have a retained stone, your first medical will be deferred for a special issuance. The good news is that subsequent exams will likely fall under AME assisted special issuance. Meaning if you meet the criteria on your next go around, the AME can reissue the certification on the spot. Much easier than most cardiac issues. Below is the section from the AME Guide pertaining to kidney stones. Note the "FAA physician" is not your local AME.
Special Issuances
AME Assisted - All Classes - Renal Calculi
AME Assisted Special Issuance (AASI) is a process that provides Examiners the ability to re-issue an airman medical certificate under the provisions of an Authorization for Special Issuance of a Medical Certificate (Authorization) to an applicant who has a medical condition that is disqualifying under Title 14 of the Code of Federal Regulations
(14 CFR) part 67.
An FAA physician provides the initial certification decision and grants the Authorization in accordance with 14 CFR § 67.401. The Authorization letter is accompanied by attachments that specify the information that treating physician(s) must provide for the re-issuance determination. If this is a first time issuance of an Authorization for the above disease/condition, and the applicant has all of the requisite medical information necessary for a determination, the Examiner must defer and submit all of the documentation to the AMCD or RFS for the initial determination.
Examiners may re-issue an airman medical certificate under the provisions of an Authorization, if the applicant provides the following:
An Authorization granted by the FAA;
A statement from your treating physician regarding the location of the retained stone(s), estimation as to size of stone, and likelihood of becoming symptomatic; and
A current report of appropriate imaging study (IVP, KUB, Ultrasound, or Spiral CT Scan) and provide a metabolic work-up, both performed within last 90 days.
The Examiner must defer to the AMCD or Region if:
If the treating physician comments that the current stone has a likelihood of becoming symptomatic;
If the retained stone(s) has moved when compared to previous evaluations; or
If the stone(s) has become larger when compared to previous evaluations.