_getFacItems return Promise《T》 so it not same as IExampleItem.
I did sample test demo in my github project below, I bind data in component not in webpart directly, while it might be helpful for you.
You can use HttpClient REST call in your SPFx web part to POST the properties to unique URL/Path to your flow.
You can find the detailed article on how to run a Microsoft Flow from a SharePoint Framework (SPFx) web part in below link:
How To: Run a Microsoft Flow from a SharePoint Framework (SPFx) web part.
Also, below is the similar example (Not in SPFx) ...
I don't know if this will help, but I wrote a blog post on the Grid layout -- complete with code samples. It uses the DocumentCard to render the grid items.
Take a look at: https://tahoeninjas.blog/2019/07/28/sharepoint-framework-design-series-layout-patterns-i/
And if there is something that you're looking for that isn't in the post, let me know ...
Yes get call is asynchrnous, you should not use render method to get data because render method will be called every time react state will changed and it will again call api causing infinite loop. for you case, on high level I think you can use below.