In order to manage Blog Search Form in Magento 2 Blog, please go to the Admin Panel > Stores  > Configuration  > Magefan Extensions  > Blog > Sidebar and find Search Form Widget section.

Search Form Widget

1. Enable or Disable the widget.

2. Set the Sort Order to manage the position of the widget on the StorefrontThe higher the number of the position, the lower it will be displayed on the Sidebar.

Once you've finished don't forget to Save Config and Flush Magento Cache.

Magento 2 blog search form configuration

3. Check the blog Search Form out on the storefront.

Magento 2 blog search form

Note: For Blog Extra edition there is available the option to include Blog Search into Catalog Search. Thus, while searching for something on your Magento 2 store customers will be able to find the blog posts related to the search query.

Magento 2 Blog Seach 

And that is how it looks like on the storefront:

Magento 2 Blog Search on Storefront