Terri,
I've never used Flixbus but hopefully one of the others can provide some information on that. In the same situation, I'd probably use one of the van transfers from Chamonix to Geneva, and then train to Lausanne. They usually drop passengers at the main rail station or the airport, whichever the passenger wants.
You'll probably have to reserve a spot on the vans, and if you're travelling with a smart phone or tablet, you can buy the train ticket online at the SBB website - https://www.sbb.ch/en .
The van transfer is only about an hour as I recall, and train from Geneva main station to Lausanne is about 45 minutes or so. This is one of the transfer services (there are others) - https://www.chamexpress.com/ .
One other point to mention..... if you're planning to visit the Aguille du Midi whilst in Chamonix, you might want to have a chat with your physician about altitude related problems. That can be a problem for some people.