We allow users to create blog entries via front end. but for some reason the tinymce editor doesn't have image upload button. Authors have to drag the image from their desktop to tinymce to insert an image.

is there a way to add image button allowing authors to upload images and using them in their blog?

No, there isn't, you will have to extend the blog module.

Hope this link helps you:

http://www.ssbits.com/tutorials/2011/adding-an-image-to-a-blog-post-using-decorators-and-the-silverstripe-blog-module/

P.S. I hope I am allowed to post that link here.