There are two options for embedding audio onto your Wordpress site.

Download the Omny.fm Wordpress plugin here and then use the "embed" block to simply copy and paste the omny.fm url for the clip you'd like to place an embed for.

Alternatively you can use the "Custom HTML" block to embed an Omny playlist or clip player. Click the "Custom HTML" block

then paste the clip or playlist embed iframe HTML code: 

And select preview to see how it looks!