Most technicians probably prefer to use dent balls to remove dents, as they do with sax and brass. They may also use a mandrel with a specialised polymer-headed hammer, but my method is far more effective... I rarely if ever use my many varieties of soft-head hammer on flutes, and the good ones re not cheap. They are commonly used to panel beat the brass instruments.
I put the flute over the mandrel, which is held in the vice.
Then I take a strip of clear acrylic sheet, perhaps 20 mm x 60 mm x 3 mm thick, with slightly rounded edges.
(Acrylic is also known under a variety of trade names, the most common in USA probably being Plexiglas. Most other plastics are unsuitable. Google may find others)
I place the strip over the dent, moving it around, while hitting it (over the dent) quite violently with a small steel hammer. This is extremely effective and cannot bruise the metal. Sometimes the acrylic breaks, but the hammer always rebounds without hitting the flute. Just be careful not to hit again AFTER the strip breaks.
Technicians are a conservative lot, and it is difficult to get them to try non-traditional approaches that work.
A FEW have listened to me and been adventurous, and been very pleased with the effectiveness of this method.
For a very large dent, start with the strip ALONG the flute instead of across it. This avoids the edge of the strip putting lines in the metal.
Most dents take about 10 seconds of hammering.
Acrylic sheet is used instead of glass for caravan and boat windows, so you may be able to track down off-cuts.
Good question. I`m happy to answer.