Is a highly reflective surface like a mirror going to reflect more of the red light than a flat red colour,
If the question is really " would the red colour seem brighter being reflected from a polished surface than if reflected from a flat surface" my view is yes, it will but only marginally.
The maximum energy level (brightness) that you can get back (reflected) cannot be greater than the energy level (brightness) that went in (incident).
"Flat" paint has an un-even surface which acts like a myriad of smaller reflective surfaces which disperse the reflected light in multiple directions. Hence the colour seems duller.
Gloss paint has a much smoother surface and doesn't disperse the reflected rays as much so you see more of them. It appears brighter than if reflected from a "flat" surface.
To raise the energy level of what is being reflected, you have to "value add" energy in the reflective process. Adding energy in that way means the lure will be much brighter than a simple "flat" lure or one painted with gloss paint.
One can liken a light reflecting process as similar to an an amplifier used in the radio frequency world. If you want more signal, put it through an amplifier and add more energy from a source of power. Convert the electrical energy from the power source into electromagnetic energy in the radiocommunications world. RF amplifiers (kickers/boosters) used in mobile phone circles are perfect examples.
If you don't have a ready power source available, then use a "passive repeater" to direct mobile phone signal into a "black spot" or similar. BUT there's no increase in energy level of the signal with a passive repeater because there's no source of electrical power from which to gain extra energy. A "passive repeater" in mobile phone circles is the equivalent to a polished reflective surface in the visible light part of the same spectrum.
Introduce a extra energy source and you have an entirely different ball game.
Part of my playing around with physical testing on this stuff, involved looking at different types of paint in a turbidity tube. Flat paint. Gloss paint and fluro all yielded different results both in terms of same basic colour with each other vs differing water murkiness.
Ditto with other colours of flat, gloss and fluro paint.
I put a LOT of work into this stuff and it took a couple of years. At the end of it I reached a conclusion.
It turns out that the conclusion I reached was the same one that a significant organisation (US Navy) plus science had reached years before BUT all were unknown to each other's work and all had different motivators.
My motivator was in terms of fishing and so I've shared the conclusion with other fishermen (you guys) and its up to you guys if you want to take notice of it.