This question showed up as one of the top results in Google and I decided to add an answer for those that may see this question later.
I have created a flow that activates on the Subscription email.
The flow is a simple email trigger, I setup the Power BI subscription to only be sent to me:

After the email arrives I initialize a String Variable and set the HTML Body to it, I then convert the HTML of the body to Text and save the Second URL to a Compose.
(This HTML step can be skipped, I am doing it to retrieve the Power BI Report Link/URL so I can include it in my Custom Email.)

The next step is to grab the Power BI Image that is included in the Subscription Email. As we know, the subscription email has a very small image and in most cases useless.
For this I initialize a second String Variable to store the Image ID:

Now we loop the attachments, the Subscription contains 1 attachment when you see it in outlook but in reality the system sees two attachments, the image attached to the email and the image in the body of the email. We are interested in the Image in the body, the other attachment is not usable.

We use a condition/If then statement to check if the attachment "Is Inline" which means its part of the email body.

And if so (if yes) we create get the Image ID and create the Email to be forwarded with a full size image and the Power BI Link:

The three very important pieces of code in the email body are to get todays Date, the URL for the Power BI Report, and the HTML Code to display the image:



You could add additional HTML Code, such as your Signature and other details.