No. Suspensions for flagrant fouls are always left up to the league office. The only offenses that result in an automatic suspension per the rule book is leaving the bench during an altercation and contacting an official.
For a flagrant 2, the rule book states:
Any player who is assessed a flagrant foul—penalty (2) must be ejected and will be fined a minimum of $1,000.The incident will be reported to the Basketball Operations Department.
Further, concerning flagrant fouls:
Whether or not said player(s) is ejected, a fine not exceeding $35,000 and/or suspension may be imposed upon such player(s) by the Commissioner at his sole discretion.