At what age do children typically reach adult reading speed?
vand den Bos et al (2002)

van den Bos et al (2002) summarises research over various ages. 
They reported:


  The reading task was to read in 1 min, as fast and accurately as
  possible, the unique and unrepeated words of a stan- dardized
  word-reading test. Results indicate that word-reading speed and naming
  speeds of colors and pictures continue to increase into mature
  adulthood.


Figure 1 (shown below) indicates that reading speed got quicker over time.



They conclude with :


  This is interpreted as supporting the the- ory that describes reading
  recognition development as a domain-specific learning process with
  reciprocally facilitating links to alphanumeric symbol-naming speed
  development.


References


van den Bos, K. P., Zijlstra, B. J., &amp; lutje Spelberg, H. C. (2002). Life-span data on continuous-naming speeds of numbers, letters, colors, and pictured objects, and word-reading speed. Scientific Studies of Reading, 6(1), 25-49.