取得した画像をそのままブラウザでダウンロードするサンプル

package main

import (
	"io/ioutil"
	"net/http"
	"html/template"
)

func indexHandler(w http.ResponseWriter, r *http.Request) {
	t, _ := template.ParseFiles("index.html")
	t.Execute(w, nil)
}

func downloadHandler(w http.ResponseWriter, r *http.Request) {
	imageURL := "適当な画像URL"
	res, _ := http.Get(imageURL)
	data, _ := ioutil.ReadAll(res.Body)
	defer res.Body.Close()
	w.Header().Set("Content-Disposition", "attachment; filename=tmp.png")
	w.Header().Set("Content-Type", "image/png")
	w.Write(data)
}

func main() {
	http.HandleFunc("/", indexHandler)
	http.HandleFunc("/download", downloadHandler)
	http.ListenAndServe(":8000", nil)
}