Integrative reduced-rank regression (iRRR) studies the predictive association between multivariate response and multi-view predictor sets. It nicely bridges sparse, group-sparse and low-rank models by exploiting a composite nuclear norm penalization. In this work, we derive an approximate chi-squared test on groups of predictors (coefficient sub-matrices), based on the estimators of both the noise level and the coefficient matrix after de-biasing from a scaled version of iRRR. The proposed method enables valid inference on view selection in multi-view learning, and it also subsumes inference procedures for lasso, group lasso and nuclear norm penalized regression estimators as special cases. Furthermore, the method is extended to allow for flexible linear constraints on the coefficients, which enables inference for a multivariate log-contrast model with multi-view compositional predictors. Simulation studies confirm the validity of the proposed inference procedure. We analyze data collected from a preterm infant study, to identify taxa of gut microbiome compositions during early postnatal period that may impact later neurobehavioral outcomes of preterm infants.