Here is a list of places where you can read free online BL magazines (all in Japanese). The chapters are free until it comes out in manga book format. I will list them as I find more and are in no particular order). Some are found on the Pixiv manga site but I have omitted those that just have sample readings that try to get you to buy the manga if you want to read the rest.
Fleur first started as free online BL novels, but then comic Fleur was born and the novel site closed. I think this is one of the first free online BL magazines and is still going strong.
Rutile magazine’s online magazine which has had some notable titles. The latest issue is free but you have to pay for the back issues.
drap free manga
There are a few free manga available on the website of Core Magazine’s drap website.
.Bloom is an online magazine you have to pay to read, but on the website there is a section where you can read original works for free.
I just recently came across this site when I was searching for the continuation of Karasu no Kachou-sama.
Various BL manga series are being serialized on this site. It also contains a section of manga by amateur manga artists. Not all are BL.
Be Boy P!
The Pixiv online magazine of Be Boy Magazine and it has quite a few original titles.
LOVE xxx BOYS pixiv
This is another Gentosha (of Rutile Sweet) free online magazine but found on Pixiv. There are quite a few titles I follow.