Publishing a blog make a lot of sense for a non-fiction work. Almost all of my last non-fiction book appeared on my blog first and this had three big benefits:

* I got me lots of feedback on the quality and interest of the ideas. 

* I got lots of criticism and discovered lots of errors and omissions in my thought and lots of places where my explanations did not come across.

* It built an audience for the book that both helped to sell it to the publisher and to promote and sell it after it was published.

I can still see a correlation (an imprecise on, admittedly) between the frequency of blog posts and sales of the book. 

All of that might work for fiction as well, but there are some downsides:

* Fiction is almost all about the execution, not the logic or the ideas. A careful and sympathetic critique partner or editor is far more likely to give you good feedback on your execution than a blog reader. 

* Most readers will not want to wait weeks or months between chapters and will lose the thread of the story if they do. 

* Putting your story on you blog counts as publication. Selling an previously published story can be much more difficult. (Unless, of course, it is a huge success and commercial publishers are clamouring to get on board. But the chance of that happening is so remote as to be discounted out of hand.)

The engagement between a story and the reader is personal. If you write a story that one person in ten loves and everyone else hates, you will have a best seller on your hands. But by the same token, you need to know where your critiques are coming from to know if they are of any value. This is why a regular in-person critique group is valuable. 

Find a critique group. If you can't find one, start one. If you can't start one, join a local writing class (most are essentially critique groups with a dedicated leader with some more or less tenuous qualifications).