In this paper, we study the marginal distribution of concomitants of k-record (KR) values from generalized Farlie–Gumbel–Morgenstern (GFGM) of bivariate distributions. In addition, the joint distribution of concomitants of KR for this family is obtained. Furthermore, some useful recurrence relations between moments of concomitants are derived. In addition, the hazard rate, the reversed hazard rate, and mean residual life functions of concomitants for this family are obtained. Some recent new measures of information, such as weighted extropy, weighted cumulative past extropy, and weighted cumulative residual extropy, are investigated for the concomitant of KR under the GFGM family. A non-parametric estimator of the proposed measure is provided by combining the empirical method with the concurrent use of KR in the GFGM family. Finally, we analyzed real-world data to examine our findings.