こちらのページと同じことを行いました。
Go言語でServerSentEvents(SSE)

フォルダー構成

$ tree
.
├── main.go
└── static
    └── index.html

main.go

// ---------------------------------------------------------------
//
//	main.go
//
//						May/19/2021
// ---------------------------------------------------------------
package main

import (
	"fmt"
	"os"
	"log"
	"net/http"
	"time"
)

// ---------------------------------------------------------------
func sse(w http.ResponseWriter, r *http.Request) {
	flusher, _ := w.(http.Flusher)

	w.Header().Set("Content-Type", "text/event-stream")
	w.Header().Set("Cache-Control", "no-cache")
	w.Header().Set("Connection", "keep-alive")

	// 1秒おきにデータを流す
	t := time.NewTicker(1 * time.Second)
	defer t.Stop()
	go func() {
		cnt := 1
		for {
			select {
			case <-t.C:
				fmt.Fprintf(w, "data: %d\n\n", cnt)
				cnt++
				flusher.Flush()
			}
		}
	}()
	<-r.Context().Done()
	log.Println("コネクションが閉じました")
}

// ---------------------------------------------------------------
func main() {
	fmt.Fprintf (os.Stderr,"*** 開始 ***\n")
	fmt.Fprintf (os.Stderr,"http://localhost:8080/\n")

	dir := http.Dir("./static")
	http.HandleFunc("/event", sse)
	http.Handle("/", http.FileServer(dir))
	http.ListenAndServe(":8080", nil)

	fmt.Fprintf (os.Stderr,"*** 終了 ***\n")
}

// ---------------------------------------------------------------

static/index.html

<!DOCTYPE html>
<html lang="ja">
<head>
<meta http-equiv="CONTENT-TYPE" content="text/html; charset=utf-8" />
<title>Server Sent Events</title>
</head>
<body>
<h2>Server Sent Events</h2>
<blockquote>
<p>count: <span id="cnt">0</span></p>
</blockquote>
<script>
    const ev = new EventSource('/event');
    ev.addEventListener('message', (e) => {
      cnt.textContent = e.data;
    });
</script>
<hr />
May/19/2021 PM 17:40<br />
</body>
</html>

サーバーの起動

$ go run main.go
*** 開始 ***
http://localhost:8080/

ブラウザーで、
http://localhost:8080/
にアクセスします。