What flying boat has the highest maximum takeoff/landing sea state?
The Grumman Albatross was capable of open sea operations and could operate in as high as ten foot seas, possibly higher with JATO rockets installed. 


  The Albatross was capable of open-ocean landings (optimally in seas no
  higher than 10 feet) due to its deep-V hull cross-section and long
  keel length, although higher seas could be downright punishing on the
  aircraft and crew. HU-16s could utilize jet assisted takeoff (JATO)
  bottles to shorten takeoff runs in rougher seas.


This Albatross pilot offers some more specifics on the certifications and says 


  Its certified for class 6 seas, which can be swells up to 10 ft. or waves up to 6 ft. 


Although he says he would not really want to do it as his operation has no need but has landed in 4ft seas. 

According to this source a Boeing 314 Clipper was successfully landed in 30 ft. seas but thats by no means regular operations. 


  The weather was far from ideal, with a big storm blowing, and 30 foot
  seas running.  But the big Boeing was successfully landed without
  damage.  The seas were so high, it was almost impossible to transfer
  the occupants to the Cutter.




I don't think anything is certified for takeoff in hurricane conditions, seaplane or not.