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 a compiled 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 (of the first chapter or two) that try to get you to buy the manga if you want to read the rest.
Comic Fleur
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 Sweet
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.
Web .Bloom
.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.
Splush
I just recently came across this site when I was searching for the continuation of Karasu no Kachou-sama.
&arche
Various BL manga series are being serialized on this site. It also contains a section of manga works by amateur manga artists of which 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.
Gene Pixiv
Pixiv page for Comic Gene. Has several BL titles such as Minato Shouji Coin Laundry, Sasaki to Miyano, Kimi ni wa Todokanai, etc.
Comic POOL Pixiv
Not all titles running in Comic POOL are BL, but there are a few notable ones.
eclair-comic
This site started off with a few titles, but the list has grown. The chapters are only free for a limited time so make sure you read them while you can. Some of the works are manga versions of novels that ran on its sister novel submissions site.
Manga Toshokan Z
A large collection of old out-of-print BL manga that you can read for free (supported by ads). You can find some classic titles here.