In this case, you cannot use a simple 'download' in html anchors.
What you can do is sending your download request through javascript.
There is an official sample for downloading.
storageRef.child('images/stars.jpg').getDownloadURL().then(function(url) {
// `url` is the download URL for 'images/stars.jpg'
// This can be downloaded directly:
var xhr = new XMLHttpRequest();
xhr.responseType = 'blob';
xhr.onload = function(event) {
var blob = xhr.response;
};
xhr.open('GET', url);
xhr.send();
// Or inserted into an <img> element:
var img = document.getElementById('myimg');
img.src = url;
}).catch(function(error) {
// Handle any errors
});