Hello, yes there are a few studies using Piagetian tasks to explore the Flynn effect and this one, for example, was indicative of similar time-lagged gains in performance as the standard approach (standard IQ-type tests, in particular those reflecting Gf and other noncrystallized abilities at the second stratum):

Fieller, A. Comparison of the development of formal thought in adolescent cohorts aged 10 to 15 years (1967–1996 and 1972–1993). Developmental Psychology, Vol 35(4), Jul 1999, 1048-1058. http://dx.doi.org/10.1037/0012-1649.35.4.1048

Abstract

Five standard Piagetian tests were administered to 180 adolescents between the ages of 10 and 15 years. The results were compared with those obtained in 1967 and in 1972 for similar participant samples. At equal ages, today's adolescents exhibited a higher level of cognitive development than the adolescents of 20 or 30 years ago. The amount of gain observed varied across tasks, being very large for combinatory thought but mixed for conservation. This acceleration of cognitive development can partially explain the continuous rise in intelligence test performance (Flynn effect). (PsycINFO Database Record (c) 2016 APA, all rights reserved)

Of further interest a couple of studies seem to indicate a subsequent reversal (anti-Flynn effect) on Piagetian tasks (much in parallell with some studies based on standard intelligence tests). See Shayer and Ginsburg (2007; 2009)

Shayer, M., & Ginsburg, D. (2007). Thirty years on — A large anti-Flynn

effect? The Piagetian test Volume & Heaviness norms 1975–2003.

Journal of Educational Psychology, 77, 25–41.

Shayer, M., & Ginsburg, D. (2009). Thirty years on—A large ant-Flynn

effect? 11: 13--year olds. Piagetian tests of formal operations

norms 1976