I attended a competition last year where one of the finalists was 24 and started at 18, and scored better than players who had been playing for 10 or more years. Some of my best students over the years have been adults. My suggestion is to set goals for yourself, and go for it!
Of course you are not too old to begin flute. You'll surely become proficient if you stick with it. It is possible to start at age 17 and become a brilliant flute player if one is motivated and attentive..
You are never too old to start the flute. I know some 60 year olds that have just started the flute. If you stick with it and practice then you are going to get better and better.