By applying redirect from your home page to a random post, you can confuse visitors. For example and especially when visitors click on a link like
www.example.com (your home page URL), they expect see your home page, not a post.
Moreover, you can also confuse Googlebot and other search engines bots (and thus SEO) if the home page is always redirected to a different post. By the way, maybe your home page is not indexed by these search engines whereas it's the most important page.
In your case, a very good option would be to keep your home page without any redirect and display a random image each day (with a link to its post). That way:
- you don't confuse visitors
- you don't confuse search engines bots (and thus SEO)
- you often change content (and image) of your home page (good for visitors and SEO because of fresh content)
For your information, Wikipedia does this with its home page (new articles and associated pictures each day). And it works well for visitors and SEO.