I'm wrong
This is a post by Avbug in a similar thread.
From the FAQ (Frequently Asked Questions) published by FAA Employee John Lynch, at the time AFS-840 of the Airman Certification Branch...who was responsible for writing and administering the regulation:
QUESTION: The particular question is whether a flight instructor who passes a flight instructor practical test (for initial issuance or a CFI rating addition or for a reinstatement) is or is not exempt from needing a § 61.56 Flight Review for the next two years, since the reg. specifically says PILOT proficiency check.” § 6l.56 d - allows this exemption for a person who has"... passed a PILOT proficiency check.." not needing to accomplish a flight review for the next 2 years.
ANSWER: Ref. § 61.56(d); If the examiner also evaluates the applicant’s piloting skills then YES, “. . . a flight instructor practical test (for initial issuance or a CFI rating addition or for a reinstatement) . . .” would meet the requirements of a § 61.56 Flight Review. However, to make sure the applicant gets credit for successful completion of the Flight Review, the examiner should record that the § 61.56 Flight Review was satisfactorily completed in the applicant’s logbook.
§ 61.56(d) states:
(d) A person who has, within the period specified in paragraph (c) of this section, passed a pilot proficiency check conducted by an examiner, an approved pilot check airman, or a U.S. Armed Force, for a pilot certificate, rating, or operating privilege need not accomplish the flight review required by this section.
QUESTION: Does a Part 141 annual check also count in lieu of a flight review?
ANSWER: Ref. § 61.56(d); As is the case in the Answer to Question 1 above, if the Chief Instructor, Assistant Chief Instructor, or Check Instructor evaluates the flight instructor’s piloting skills then the answer is YES, a Part 141 annual check would count for a § 61.56 Flight Review. However, to make sure the applicant gets credit for successful completion of the Flight Review, the Chief Instructor, Assistant Chief Instructor, or Check Instructor who conducts the check should record that the § 61.56 Flight Review was satisfactorily completed in the applicant’s logbook.