For fresh water it would appear that Navicula acceptata is the fastest. It has a reproduction rate (under the best of conditions) of 3.8 times per day:
If you include cyanobacteria under your definition of microalgae, then Synechococcus UTEX 2973 which as a doubling time of 1.9 hrs, or 12.6 doubling periods per day.
Chlorella sorokiniana, similar doubling time to Synechococus UTEX 2973 as Matthew B Paddock mentioned in acetate enforced media. Most consistent fast growth can be observed in Dunaliella sp.