Luckily, this blog post provided a solution. The author writes:
One of the great features of Picasa Web was that you could embed a Flash slideshow of your albums. Google would even give you the code to do it. There was a button that said Embed and it would give you the code. Just cut and paste and you were done.
With the migration to Google Plus Photos, this disappeared.
Here's a work around.
Use the following link to get back to the original PicasaWeb site:
Hopefully the embed button makes a re-appearance, or Google leaves the old page up forever.
He also offers an alternate solution, if you want to go check it out.