But it is legal to wrap true flexible arrays in a struct that has at least 1 other non-true-flexible array, including an empty anonymous struct (i.e. taking up no size).

struct obj {
       ...
       union {
               struct {
                       struct { } __unused_member1;
                       struct foo name1[];
               };
               struct {
                       struct { } __unused_member2;
                       struct bar name2[];
               };
       };
};

This is not legal for multiple reasons.

C99 6.7.2.1p2 says

the last member of a structure with more than one named member may have incomplete array type; such a structure (and any union containing, possibly recursively, a member that is such a structure) shall not be a member of a structure or an element of an array

Additionally, struct {} is not valid C syntax. The grammar is

struct-or-union-specifier:
                  struct-or-union identifieropt { struct-declaration-list }
struct-declaration-list:
                 struct-declaration
                 struct-declaration-list struct-declaration
struct-declaration:
                 specifier-qualifier-list struct-declarator-listopt ;

so we need at least one struct-declaration to form a struct-declaration-list. Even if this were valid syntax, 6.7.2.1p7 says

If the struct-declaration-list contains no named members, the behavior is undefined.