This is related to How do I remove code duplication between similar ref-qualified member functions?, but there's a bit more work needed. In short, we want to forward ref-qualified versions of iterate on to a static member function, which can appropriately forward on the individual elements of buf. Here's one way to do it:
template <typename P>
class Frame {
    std::vector<P> buf;
    template <typename F, typename Iter>
    static void iterate_impl(F&& f, Iter first, Iter last) {
        while (first != last) {
            f(*first++);
        }
    }
public:
    template <typename F>
    void iterate(F f) const& {
        iterate_impl(f, buf.begin(), buf.end());
    }
    template <typename F>
    void iterate(F f) & {
        iterate_impl(f, buf.begin(), buf.end());
    }
    template <typename F>
    void iterate(F f) && {
        iterate_impl(f,
            std::make_move_iterator(buf.begin()),
            std::make_move_iterator(buf.end()));
    }
    template <typename F>
    void iterate(F f) const&& {
        iterate_impl(f,
            std::make_move_iterator(buf.begin()),
            std::make_move_iterator(buf.end()));
    }
};
Another way to approach it is to have a forward_like function:
template <typename T, typename U>
struct copy_cv_ref {
private:
    using u_type = std::remove_cv_t<std::remove_reference_t<U>>;
    using t_type_with_cv = std::remove_reference_t<T>;
    template <bool condition, template <typename> class Q, typename V>
    using apply_qualifier_if = std::conditional_t<condition,
        Q<V>,
        V
    >;
    static constexpr bool is_lvalue = std::is_lvalue_reference<T>::value;
    static constexpr bool is_rvalue = std::is_rvalue_reference<T>::value;
    static constexpr bool is_const = std::is_const<t_type_with_cv>::value;
    static constexpr bool is_volatile = std::is_volatile<t_type_with_cv>::value;
public:
    using type =
        apply_qualifier_if<is_lvalue, std::add_lvalue_reference_t, 
        apply_qualifier_if<is_rvalue, std::add_rvalue_reference_t,
        apply_qualifier_if<is_volatile, std::add_volatile_t,
        apply_qualifier_if<is_const, std::add_const_t, u_type
    >>>>;
};
template <typename T, typename U>
using copy_cvref_t = typename copy_cv_ref<T, U>::type;
template <typename Like, typename U>
constexpr decltype(auto) forward_like(U&& it) {
    return static_cast<copy_cvref_t<Like&&, U&&>>(std::forward<U>(it));
}
Which you can then use in the implementation of iterate_impl:
template <typename P>
class Frame {
    std::vector<P> buf;
    template <typename Self, typename F>
    static void iterate_impl(Self&& self, F&& f) {
        for (int i = 0; i < self.buf.size(); ++i) {
            f(forward_like<Self>(self.buf[i]));
        }
    }
public:
    template <typename F>
    void iterate(F f) const& {
        iterate_impl(*this, f);
    }
    template <typename F>
    void iterate(F f) & {
        iterate_impl(*this, f);
    }
    template <typename F>
    void iterate(F f) && {
        iterate_impl(std::move(*this), f);
    }
    template <typename F>
    void iterate(F f) const&& {
        iterate_impl(std::move(*this), f);
    }
};