Once you have identify the blocks, you can take gene pairs (Homoeologs), select homologous genes in close related species and do a phylogenetic analysis, for example following the methodology published in Egan et al. 2010 for soybean (http://sysbio.oxfordjournals.org/content/59/5/534.short). There are two main approaches:

1) Global and genic clock method, using the Ks of the gene pairs (Lynch and Conery, 2000, http://www.sciencemag.org/content/290/5494/1151.short).

2) Relaxed clock method, using Maximum Likelihood (ML) method penalized likelihood (PL) with R8s (http://loco.biosci.arizona.edu/r8s/)(Sanderson 2003, http://bioinformatics.oxfordjournals.org/content/19/2/301.short) or using Bayesian inference with BEAST (http://beast.bio.ed.ac.uk/Main_Page) (Dummond and Rambaut, 2006)(http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.0040088).

Good luck !!!

The Brassica rapa genome paper http://genomebiology.com/content/10/10/r111 uses the Ks method to estimate the date of the recent polyploidy event in rapa. Assuming you believe their analysis, you could assume this date, and apply it to other Brassica species, or even use a number of methods and species to arrive at a consensus.

Do you know if the blocks you are interested in are a result of this recent event?

Absolute dating through molecular clock based approaches is not valid as for as the duplication age estimation of large genomic blocks are concerned, because each subsegments of such blocks is under different functional constraints and thus evolving differently. Only relative estimates are possible through phylogenetic analysis of subsegments of such blocks. For details please see, following

Fourfold paralogy regions on human HOX-bearing chromosomes: Role of ancient segmental duplications in the evolution of vertebrate genome:Molecular phylogenetics and evolution 2013