Like indicated in Chris' answer, you can automatically rebuild your app when using ng build --watch.
If you just want to serve the latest version of your app, you can disable caching from http-server (which is on by default), using -c-1 option (doc)
On linux (use single & to run scripts in parallel)
"start-dev": "ng build --watch & http-server -c-1 dist",
On windows (notice the start command):
"start-dev": "start ng build --watch && start http-server -c-1 dist",
Notes
Your browser has probably already cached the files dist before you deactivate the cache like above, so clear the cache manually once. You won't need to to that after
This solution will not reload the page, you have to do it yourself
http-server does not support fallbacks, which might be a problem if you are using angular's default strategy. So if you were on http://localhost:8080/module1/path1 and you reload the page, you'll get a 404.
You need to reload http://localhost:8080 and navigate to the correct url from the app router
Depending on your angular.json, the output folder might be dist, dist/projectName, or dist/projectName/browser, or whatever you indicated
start-dev: ng build --watch && http-server -c-1 dist? This should prevent caching from serverng serve --prod