No, recording something off a different source is pretty simple.
You need: 1 audio cable connection. Done.
I don't know about your source device (your turntable), but I assume it has an
audio out in form of an audio jack and not only the red/white wires for direct speaker hook-ups. Then you just connect that cable from your turntable to the computer's
line-in and set up Audacity to record from that source (else it might try to record system audio or from the microphone). I think you can also use your microphone input, some devices like Macs don't seem to make a difference of a "Line-In" and "Mic" socket (my MacBook back then didn't at least), but I heard that on some OS the microphone socket gets some gain to boost speech clarity, and this gain might cause clipping in recording.
The biggest problem of recording audio is the interfaces/links you add. E.g. if you have a simple connection like Turntable <-> Cable <-> Computer, you have 3 interfaces. And each of it can introduce sound-altering effects. For example, my old jack-to-jack cable I used to record my compact cassettes would add a hum (deep bass) to my recordings, the other time the sound output socket was a bit funny and would "fizzle" once in a while, adding this fizzle to the audio transported and recorded to the PC. I heard LP rips where the turntable would add noise to (you could hear a clear, rhythmical rumble, albeit quiet in the audio and only audible in silence, but this is still altering the files). And often, especially with poorly designed computers, the onboard soundcard might be "dirty" by picking up statics due to the lack of shielding. A modern graphic card running at full power for example can alter the ability of line-in recordings. It's all pretty much science/physicks about electricity and the likes. How to check if everything's right? Do a test recording with no sound output of the source device. If the volume meters of your operating system or in Audacity does only twitches a tiny bit deep in the -50dB area, that is all still fine.
In Audacity you should test your input meters to avoid clipping. So you both need to balance Audacity's recording level (how loud the software itself will record) as well as the output level of your turntable. If you try to "virtually" bump up an audio signal software-sided it will sound more and more nasty as it will just make the noise worse, so your first thing is to twist the knobs on your turntable so there is enough "actual" audio signal coming from the source. If the PC gets enough audio juice, you often don't need to adjust Audacity's recording up, rather the opposite, you often want to tame it a bit. Make sure you have some dB left to the maximum signal input, e.g. 3 dB underneath. The colours of the Audacity volume meters are a good indicator. Also, make sure you don't have any EQ settings enable during recording, neither on your computer, nor your source device.
Upon exporting to FLAC, make sure you select 16-bit, else you waste disk space as said in another thread. A LP can, at best, keep audio signals worth of around 12-bit. Hence why the CD was invented, and the CD that surprasses a LP has "only" 16-bit. Exporting in 24-bit is pointless.
Also, you see why recording is much more tricky than ripping. "Ripping" is used when you source your digital audio on the same system without any links like audio cables or other devices in the middle, e.g. ripping a music CD as it's done on the very same system you work with that file. A "recording" is what's introducing all these links you have to care about (other devices, cables, cable connections, meters to match). So actually, you can never "rip" a vinyl. It is nitpicking on that term, but it's still wrong
