Are you looking to strum and accompany, or have two independent lines running together as a duet? If the first, then any flute solo with chords marked in the piano accompaniment will work.
If you want a true duet, I'd look at some oboe duets and also alto saxophone, which keeps the range from going into the super high flute range. No transposition necessary. I have some alto, oboe and flute duet stuff if you are looking for something along that line. I also have some Disney flute solos and the piano part may may have the chords written in.
I would suggest you run with something your son can already play to start with. I am sure if he tells his band leader what you want to do they will be happy to write some chords above his music (in fact I think they would be ecstatic that he's got a parent who will really encourage him to practice!). Good luck with it, music is a fabulous activity to share with your kids.
My wife plays flute and I play trumpet. I do some arranging for duets that we play. I'll skip the transposing stuff. The flute part almost always has to be raised an octave. Even though the uke range could play the flute part, it's a royal pain to read music in ledger line heaven for me. If I played up there all the time I would be used to it. Playing in the staff is pretty low for the flute--especially the lower staff. Thankfully, my wife can play up an octave without me having to write out a score for it each and every time. Unless your son plays by ear or from memory. He will have to read from sheet music. What has really worked for us is fake books and there are literally over a hundred of them out there. What you want is a "C" fakebook if you go that route. If you just look for a specific song, there are sources on line that can be downloaded for a price. Some are only 99 cents though. Fakebooks are a much better buy than buying individual songs one at a time. I wish you the best in finding music for you both. Playing with family is really great fun!
Call your local music store - one that deals with band instruments - and ask them to find an easy flute solo book that also has the chords written in. That way, your son can play the flute solo and you can strum and accompany. You will both be playing in the same key, so no need to transpose.
Some books will have a piano accompaniment, and that as fine, but again, you want those chord names written in above the measures. There are easy flute solo books out there - movie favorites, easy renditions of the classics, John Williams, popular songs.... Tons. I have the 1-800 number of my local music store and they can find just about any music out there. If you don't have a local one, I will be glad to give it to you.
Look at the closeup of the music on this one. You see the flute solo is the top line, and the two bottom staves are the piano accompaniment. And the chord names are written above the piano part. JW Pepper is also a wonderful resource.
http://www.jwpepper.com/10045983.item#.U4kJ1F7oa8p This book would be great if I could see the piano part and tell if the chords are written in. Your son could get the flute book and you could use the piano book. You could call and ask.
I'd ask your son what song that he may already know, or is motivated to learn, he wants to play, and then look online to find the chords for it in the same key.
I'd ask your son what song that he may already know, or is motivated to learn, he wants to play, and then look online to find the chords for it in the same key.