The Object Oriented Fortran features supported in dbx are type extension and polymorphic pointers, which is consistent with C++ support.
The dbxenv variables output_dynamic_type and output_inherited_members work with Fortran.
You can use the -r, +r, -d, and +d options with the print and whatis commands to get information about the inherited (parent) types and the dynamic types in Object Oriented Fortran code.