Yes, you can, and I have, as evidence. I flew a very similar route, from Austin to Phoenix, and then on to San Fran. I've also done other internal flights. All on the Visa-Waiver Program.
The visa-waiver is a check done at the international border, as you enter the US from another country. Once you're within the strict US border, you're permitted to travel (legally) however you want, wherever you want.
You may still be asked to present your passport as identification for flights, but the visa-waiver aspect won't be checked by immigration - it's simply an ID check by ticket and gate agents at the airport.