[...] I am looking for a player that can read CD's and play digital FLAC files. [...] How do you guys enjoy your FLAC music at home?
When it comes to technical stuff I usually take a modular approach, meaning that a combination of dedicated devices is preferrable to all-in-one devices.
You seem to be wanting the latter, and I advise against that. If you believe that an integrated device for a few hundred euros/pounds/dollars -- containing amplifier, data storage, CD transport and D/A converter -- can actually sound great, there is a bridge I'd like to sell you.
Everybody already has a player that can play CDs as well as FLAC files. It is called "computer". I totally get it why one would wish to use an extra device -- I do, primarily because of fan noise -- but I've never seen one that wouldn't be a downgrade soundwise. Navigation is a problem as well with their little displays.
My stereo system has pre-amp, power amp and CD player (NAD Monitor series). Connected to it is a wireless external D/A converter (Audioengine D2) that plays the FLAC stuff coming from the computer and that is capable of processing anything up to 24 bits and 192 kHz resolution.
The modularity of the system lets me exchange any component for a new one if I wish to further improve the set-up. And if something breaks I don't need to replace everything.
The main reason, I think, why CDs have a bad reputation is that regular CD players are just not very good. The difference in sound quality between the usual players for around 500 euros and one for 1500 euros (which would be about the price of my CD player if it was still available new) is quite remarkable. 500-euro players invariably sound mushy, but you'll never know it if you don't make the comparison.
The D2 D/A converter (600 Euros) is about as good as the NAD 5300 CD player.
If I hadn't had the wireless requirement I would have gone for a D/A converter from a Chinese high-end manufacturer. For a similar price they can be even better than the D2.
When my CD player gives up the ghost I will probably replace it with the (vintage) Sony SCD-XA777ES or with a vintage Cyrus Mission player. Or maybe just a CD transport that I plug into the D/A converter.
I hope this does not come across as if I threw a lot of money at music reproduction, because I don't. Everything I have except loudspeakers and the D/A converter was very cheap because I bought it used.
TL;DR >> Consider avoiding integrated hi-fi devices. Get a good D/A converter. Buy used.