Advice and suggestions please

Current system is vinyl only:

LP12/Keel/Radikal/Ekos/Akiva NAC52/Supercap/NAP250 Linn Isobariks

I only have a handful of CD's but my 'other half' has quite a number and would like to be able to play the music through my system.

Can you advise on the most cost effective way (in other words least cost that will not sound nasty through the Naim kit) to add FLAC quality streaming to my system?

If it's relevant - we are a completely Apple house