Since VARs can be estimated as independent equations, omit -auto could be used.  Or you could apply a OLS stepwise selection method to each equation, or use AIC or BIC to select the best specification from a set of candidates.  Maybe someone has a script to perform the steps, but I doubt anyone has set this up to be as simple as --auto.for a system of equations. 

One reason you may not find anything as simple as an --auto option for VARs is that data mining of this type (setting zero restrictions) is counter to the VAR modelling philosophy. Also it is rarely necessary because setting lag coefficients to exactly zero when the OLS estimates are statistically similar to zero will typically have few statistically discernible effects in the performance of the entire system (that's why they are statistically insignificant).

GRETL does have a VAR lag selection tool that does not violate the general VAR model building concept, but this is probably different from what you desire.  Lasso in R might be the most reasonable alternative, especially if you are using the VAR to forecast.  

Or consider  Bayesian VAR  modeling that lets you shrink the lagged coefficients toward around priors that are centered around zero.  Check out Nobel prize winner Chris Sims R code to implement (http://www.princeton.edu/~sims/#VARtools)