Updated/fixed version for: https://gist.github.com/L7R7/46615daa6d1a41d0499c261db8a2f3bb

Reader2.scala

package com.l7r7.lab.feed.client

import akka.actor.ActorSystem
import akka.http.scaladsl.Http
import akka.http.scaladsl.model._
import akka.http.scaladsl.model.headers.Link
import akka.http.scaladsl.unmarshalling.Unmarshal
import akka.stream.scaladsl.Source
import akka.stream.{ ActorMaterializer, Materializer }

import scala.concurrent.{ ExecutionContext, ExecutionContextExecutor, Future }

object Reader {
  implicit val actorSystem: ActorSystem = ActorSystem()
  implicit val materializer: ActorMaterializer = ActorMaterializer()
  implicit val executionContext: ExecutionContextExecutor = actorSystem.dispatcher

  def read(initialRequest: HttpRequest): Source[(HttpResponse, Multipart.General), _] =
    Source.unfoldAsync[Option[HttpRequest], (HttpResponse, Multipart.General)](Some(initialRequest))(Crawl.crawl)

  def main(args: Array[String]): Unit = {
    val initialRequest: HttpRequest = ???
    read(initialRequest)
      .map(_._2)
      .flatMapConcat(_.parts)
      .runForeach(p => println(p.entity.contentType))
  }
}

object Crawl {

  def crawl(reqOption: Option[HttpRequest])(implicit actorSystem: ActorSystem, materializer: Materializer, executionContext: ExecutionContext): Future[Option[(Option[HttpRequest], (HttpResponse, Multipart.General))]] = {
    reqOption match {
      case Some(request) =>
        Http().singleRequest(request)
          .flatMap(response => Unmarshal(response).to[Multipart.General].map(multipart => (response, multipart)))
          .map {
            case tuple@(response, multipart) =>
              if (response.status.isFailure()) Some((None, tuple))
              else nextRequest(response, HttpMethods.GET).map { case (req, res) => (req, (res, multipart)) }
          }
      case None => Future.successful(None)
    }
  }

  val baseUrl: Uri = ???

  def nextRequest(r: HttpResponse, m: HttpMethod): Option[(Option[HttpRequest], HttpResponse)] =
    Some((nextLink(r).map(url => HttpRequest(uri = baseUrl.copy(path = url.path))), r))

  def nextLink(r: HttpResponse): Option[Uri] =
    r.headers[Link]
      .map(_.values)
      .filter(_.size == 1)
      .map(_.head)
      .filter(linkValue => linkValue.params.head.key == "rel" && linkValue.params.head.value() == "next")
      .map(_.uri)
      .headOption
}