Flat fee is easiest. Why confuse your customer, and perhaps even raise the question that you might be upselling a tad just to make a few $$$ at their expense.

BUT ....

... the only time that I can think where it might play negatively is where somebody may think, "That son of a gun charged me more than the other guy!" not realizing that you built in travel. Unless they mention it to you, you will never know. Is this likely to happen? Who knows ...

DON'T TELL ANYONE about a charge for mileage. Keep it to yourself.

Before I retired, I'd tell anyone who opened a call with "how much is your show?" that each show is priced individually according to the client's needs, location, etc. (The 'etc' would secretly include whether this was a holiday season or other high-demand season, and whether the show they wanted fit into a convenient pattern with an existing engagement, like an hour later and a mile from an already-booked show).

Then I'd do my figuring quickly in my head, based on the size and length of show, travel requirements and the other factors I've just mentioned, including a little 'flex' to allow me in need to offer a small discount as an incentive. ("I COULD offer you a $25 discount if you book today and get me a 50% deposit by [date].")

As a professional speaker, I charge my speaking fee PLUS travel.

As a magician, I have not yet begun to do much travel...but I would think that the same formula would work. In fact, I am going to combine my skills as a Catholic speaker and an illusionist on some occasions...a whole new dimension to my ministry.