I believe that one can become what one believes. The more embodied our beliefs are the more we can be the way we want to be. The more we embody desirable beliefs the more we are likely to take action because our body is more used to feeling the subtle and not so subtle vibrations, feelings and emotions associated with the thought.
Prayer is done at least 3 ways; silently, out loud and on fabric that is hung up for all to see.
Done silently, prayer often slows the breathing rate. This makes one more relaxed and receptive to new ideas or those highly desired. The alpha state is more present and we become more creative, suggestible or open to the ideas within the words of the prayer.
To me it seems that the more I engage my body and thinking together (mind/body) that there is a better possibility of the idea making more of an impact in the way I experience the prayer and become more connected to it energetically either as a process of connecting directly with my higher power and or a specific piece of information that I need to direct my actions.
For many, speaking out loud while praying has the effect of strengthening the mind body connection with the spoken idea(s). There is tremendous power in the energy of the human voice, the power of that sound. Thoughts when spoken can become more embodied, they are often more real to the speaker because they have the extra connecting energy of the throat/sinuses/chest/back/belly/heart vibrations. Try singing a song out loud and singing it silently and you may get what I am referring to. Listen to a great Gospel singer like Mahalia Jackson, Aretha Franklin or Tremaine Hawkins and feel the full force of spirit in action. Silence may be golden but as Goethe said "boldness has a genius, magic and power to it".
There is a certain amount of throat and speech activity (sub-vocalization) while thinking but prayer-wise I prefer the spoken form however the silent form is certainly serviceable to many others.
But for me praying strong and out loud seems to have more impact on my inner being. It makes me feel that I am heard more and the outspokenness as well gives me a better sense of my being heard. Some songs are actually prayers or affirmations via strong sound.
I have a Tibetan prayer flag. Not sure what it does and I just do not relate to it as much as vocalized prayer. I respect it though, I just do not pay much attention to it.
Try this for yourself. When you pray, or for that matter, sing, make it loud. Engage more of yourself and let your prayers "be heard". If your prayers are not getting answered then repeat them more often and perhaps louder. The quality of your thinking guides the energy of the breath. Breathe in spirit (inspiration) think of it as holy and you have Holy Spirit.