A binaureal beat is created by playing a different tone in each ear, and the interference pattern between the slightly differing frequencies creates the illusion of a beat. It's intended to be heard through headphones, so there's no cross-channel bleed across both ears. Listen to this, I'll play a simple binaural beat, and I'll slide the pan control back and forth from one ear to the other. You can see that there isn't actually any beat, it's just an acoustic illusion:
You are already far beyond the need for using an entrainment product as a meditation aid. Those who sincerely believe this to be the case would not have come searching for a meditation site such as Project Meditation to help them learn and practice meditation and brainwave entrainment. They would probably not even bother with using an entrainment aid; hence this entire discussion would be irrelevant to them. The fact that you are here, reading this, seeking to benefit from incorporating meditation and brainwave entrainment to aid in your existing meditation practice suggests you are not one of these folks whose development is so advanced that entrainment is of no use to you.
Why not? Because the flushing has nothing to do with the brainwaves or entrainment, and everything to do with the expectations we bring to the use of entrainment. We didn’t watch that sunset with any expectations of face flushing. We didn’t have any of those expectations while listening to that music. In short, there is a cause generating the effect, but the cause is our expectations, (excellent Article here) not the entrainment.

Whenever we become very relaxed and the usual chatter of the mind slows down a little bit, if we remain aware and do not slip into sleep or unconsciousness, we begin to perceive things that we had not noticed before. This is slightly different than the issue of “expectations” discussed previously, although a relationship to them can develop which will be discussed below. These have to do with the fact that in our typical state of consciousness our mind is racing so fast and so loud, and our body is so engaged with activity and physical tension, that we are unaware of some subtle perceptions that are there all the while, but which get buried beneath all the physical and mental noise.
In addition, Western culture reinforces thought and communication styles associated with the left brain hemisphere, which controls logic, language, and linear thinking in a majority of people, as opposed to the right hemisphere which controls brain centers for emotional, intuitive, creative, and non-linear thought processes. Note that a significant minority of people has the opposite hemispheric dominance than the majority of people.
Listening to brainwave entrainment music will provide you with the benefits of a formal meditation practice. It will improve your mental clarity, your creativity and your ability to learn and to concentrate. It will bring you peace of mind and emotional stability. It is also one of the most powerful natural ways to cure insomnia and can dramatically improve the quality of your sleep.

If brainwave entrainment leaves you with unwanted side-effects (see below) or discomfort, you’re probably encouraging a range of brainwaves that are already excessive in some area of your brain. The way around this is to get a brain map to see what your brain’s strengths and weaknesses are, and see what (if any) brainwaves could use some encouragement.