how do I play flac files on my mac computer?

There is no direct way for iTunes to play FLAC files. They need to converted to AAC,Mp3 or other. The convertor I've been using lately is XLD http://tmkk.undo.jp/xld/index_e.html and its free.

Have you tried Vox? https://itunes.apple.com/jp/app/vox/id461369673?l=en&mt=12

It plays FLAC files (and just about anything else) - though not in iTunes. No need to convert anything.

It will lose quality when you do the conversion, right?

Converting from FLAC, (Free Losless Audio Codec) to mpg or other lossy file type will reduce size and quality. There are many many factors involved in determining how much of each. If you convert to Apple lossless (ALAC) will not lose quality.

You cannot play FLAC files natively in iTunes out of the box. There are ways around it, however.

1. You can convert FLAC files to ALAC with these step-by-step instructions using XLD. It's free and works great.
2. You can use a third-party software (like iRiver) to play FLAC files natively while also maintaining your iTunes library. It's not ideal but it works.

In case you're wondering, converting FLAC to ALAC is the way to go. It's simple and painless. There is no quality loss when converting FLAC to ALAC and you can read about that here too.