May I ask why you are wishing to stick with vinyl>FLAC>CDR for your music library?
Since, I think you are saying that your vinyl are already (being?) converted to FLAC (before to *.cda > for burning CDRs)?
Have you considered a NAS library? Or, have you considered a DAP? Or, have you considered a small DAC dongle?
I hope you are aware that the some of the audio qualities associated with vinyl provide much less 'fidelity' than CDs,
I also hope you realize that vinyl conversion to digital -using a less than stellar performing turntable and improperly aligned cartridge- will further degrade the results (whether FLAC or MP3) and possibly make the outcome less desirable.
Ok, here goes.
Lets get some fundamentals out of the way before I ramble about my musical journey.
1) I'm fully aware of the 'fidelity' when comparing vinyl to CD/digital. No need to convince me there at all. Vinyl is no longer my preferred format, and hasn't been for many years.
2) I'm not burning my vinyl onto CDR's. I'm ripping it to CDRW's, converting to FLAC, rinse and repeat. I don't listen to CDR's.
Now's the time for TLDR merchants to bail out, btw.
I grew up in the vinyl and cassette era and had built up a reasonable vinyl and tape collection before CD's came into being. My vinyl collection is 90% Reggae. As well as playing my vinyl, I used to record it to cassettes to play in the car, share with friends, and later do mixtapes. I also used to record the very very few Reggae shows on the radio then onto cassette, and also buy Sound System tapes (it's a Reggae thing).
Forward onto the birth of CD's. I was a slow adopter for a couple of reasons. In the early days, a lot of music I wanted wasn't available on CD. Once more and more of it was getting released onto CD's I was faced with two 'problems'. Firstly, they would give you a couple of bonus tracks on a CD album compared to the vinyl. I resented that at the time as it felt like manipulation to convert people onto CD (I later realised it was as much to do with more space available on CD as it was to do with manipulation) Having then caved into buying CD's, I had decided I didn't like the 'clinical' and 'cold' sound of digital compared to vinyl. Yep, been there, got the T shirt, lol.
As the years passed I was buying less and less vinyl and more and more CD's, especially as I was now buying more and more Jazz and 'World Music' and other genres (still no Rock & Pop) and less and less Reggae. I was also beginning to realise two things around sound quality, too. Digital recordings were much 'cleaner' than my vinyl and basically now sounding much more satisfying to my ears. Sitting down listening to music, I was now sold on CD's as the way forward. I also realised a lot of Reggae, especially of certain eras, wasn't necessarily recorded too well, but that's a whole other subject.
Forward onto streaming. Just before lock down time, I eventually bought myself a Yamaha network amp and an annual Deezer subscription. Wow!....revelation time! This has felt in many ways like a having a record shop in my front room, and on the go. I can search for stuff I've heard on late night Radio 3 for example, and nearly every time the album will be there. With my Reggae vinyl, a lot of it is on Deezer, but certainly a fair percentage of it isn't.
So why am I bothering to rip my vinyl to Flac?, and do I have a NAS library or DAP?...
Firstly, I've begun the process of very slowly selling off my vinyl, beginning with the stuff I'm no longer as excited by, and some of the more expensive stuff. I thought I'd sell off the whole collection at one point, but soon realised that there's stuff in there I don't want to part with. Instead, I'm slowly working through it, cleaning it all up and ripping as I go. The stuff I have sold has been 'reinvested' into a variety of new headphones and iems. The collection that's eventually left will be nice and clean and there as my legacy when I'm gone. It should still be worth a few bob and one of our kids knows what she's doing with vinyl
I have a few DAP's, my favourite being the ibasso DX300. I often listen to music on it with a varied collection of headphones and iems so as not to disturb others in the house. I have my entire CD library ripped as Flac files and my vinyl collection is being added as I go. I can listen to it all on my DAP's. It's backed up on various old laptops and external hard drives. As for a NAS?...I also have a Wiim pro going through the hifi and can access my entire library via the Wiim app on an Android tablet with an external sd card, as well as access Deezer. In short, I have multiple ways to listen to my vinyl and CD collection, as well as Deezer streaming. I listen to a lot radio, too, so I'm really spoilt for choice these days! Archiving my vinyl collection is time consuming and can be labourious, but it's also nice reaquainting myself with it and bringing back old memories.
I appreciate your questions and take them in good faith. I like giving a detailed response. One of the minor faults of this excellent forum for me is a little bit of, otherwise well intentioned, scientific arrogance, for want of a better term. Examples being... why listen to vinyl when it sounds rubbish compared to digital?...why waste money on a DAP when an old phone and dongle gives the same, if not better, results?. I appreciate these type of questions and responses are given here in an attempt to help people get the best technical performance and bang for their buck, and that's nice. However, we should also remember that music appreciation and the gear that goes with it is a hobby motivated by love, and love takes many and varied forms and is most often ruled by the heart, not the head. There's a thousand and one use cases, and everyone will likely have their own little set up that works for them. This is my set up, and it works for me.