My guess is this is how the timeline works-
Fall/Winter 2014: Daredevil S1
Spring/Summer 2015: Jessica Jones
Fall 2015: Daredevil S2/Luke Cafe
Winter 2015: End of Daredevil S2
That's more or less what I came up with, but I had it somewhat differently.
Namely,
Luke Cage
begins just after ".380" but before "A Cold Day in Hell's Kitchen". In Claire's first episode here, she tells her mom about The Hand's attack on the hospital, and it sounds like it's been a week or two since the attack.
Meanwhile, there's Turk's line after watching Stokes throw Tone off the roof: "You Harlem neggas are off the hook. I'm going back to Hell's Kitchen where it's safe." Given Turk's status as the resident chew toy, and the way that line is written, it makes sense to see that line as wishful thinking on Turk's behalf: he returns to Hell's Kitchen after watching Tone get murdered, thinking "the Hell's Kitchen crews that haven't been wiped out by the Punisher are so much better than Stokes".and then gets kidnapped by The Hand and almost loses his foot when Karen uses his tracking bracelet to alert the cops.

Luke Cage is set at least 5 months after Jessica Jones. It also takes place simultaneously with the tail-end of Daredevil Season 2.
The real question is how much time passes between the two seasons of Daredevil. Fisk mentions in S2 that he first met Murdock 'several months ago'.
My guess is this is how the timeline works-
Fall/Winter 2014: Daredevil S1
Spring/Summer 2015: Jessica Jones
Fall 2015: Daredevil S2/Luke Cafe
Winter 2015: End of Daredevil S2
Formerly sn939

Luke Cage also takes place
at the same time
as Daredevil season 2.
Part of the series takes place simultaneously with the events of the second season of Daredevil, as Cox noted after Claire Temple first appears in that season, she has "a cut in her eyebrow", which she receives due to events in Luke Cage, adding, "the timeline had been thought through and worked out so that whatevers going on in Luke Cage somehow at some point during that show, the next day shes in the hospital talking to me [in Daredevil]."

Luke Cage season one takes place after Jessica Jones.
If it's all the same to you, I'll have that drink now.-Loki (Marvel's Avengers)

It would be odd for him to leave Hell's Kitchen just to represent Cage in Harlem. Plus, I doubt that Hogarth would like to mess with Mariah and her contacts.
I once told a man to go screw himself! Can you even imagine?! - Kilgrave

The chronological order is the same as the order the seasons are released on Netflix. So, Daredevil's 1st season, Jessica Jones, 2nd season of Daredevil, Luke Cage.
I wish Foggy had show up as Luke's lawyer in the last couple episodes. That would have been a nice tie-in.
There's always free cheddar in the mousetrap

I like how a few trolls couldn't help but inject opinions no one asked for.
"I am just a grain of sand on your beach" - FNM

Absolutely..Marvel have screwed both these showsjust one big beep yawn..can we get The Punisher going now guys.because Jones and Cage suck balls
Deputy Davo's Pig Squeezing Country and Western Comedy Show.

Who cares? JJ is awful.

Ding Ding Ding!

It is 6 months after JJ kills Kilgrave. Luke has been working with Pop for 5 months. This was mentioned in the show.

Hmm I never caught that detail (the first one you mention).
Reading my signature constitutes admission that I am correct. (Too late)

She has a cut on her face that she got during the hospital attack so it has to be very soon after. She's also just moving back home with her mom after quitting her job.

"right after" or just "after"?
I have seen some people suggest it can't have been very long but I'm not sure where they're getting that. But I've only watched LC one time through so may have missed a few details.
But yeah, it's clearly after one way or the other.
Reading my signature constitutes admission that I am correct. (Too late)

When Luke meets Claire it's right after
the ninja attack on the hospital from DDS2

Yeah I don't think it's "immediately". But I also don't think anything particularly significant happens in between so maybe it's not super relevant.
All MCU projects essentially happen in the order they come out and roughly (sometimes very roughly) at the same time they come out. The Netflix shows are a bit unique in that the whole season drops at once though the events can take a while to play out.
So I think we can all agree this is after JJ, how long after is a bit harder to be exact about. I think the events of DD2 happen in between.
Reading my signature constitutes admission that I am correct. (Too late)

If something was giving me a headache 4 days later I'd be surprised I was still getting headaches from it.
Particularly if I was the bulletproof Luke Cage.

Death is the road to awe.

He also mentions in the first episode that he "still gets headaches" from Jessica's shotgun blast to his head. Doesn't seem like it'd be that great a surprise if it happened recently.
"The plastic tips at the end of shoelaces are called aglets. Their true purpose is sinister."

He barely met her for like 5 minutes when he was conscious in JJ.

Immediately implies that Jessica Jones begins and Luke Cage begins right away. There's definitely some passage of time there though. Cage had trouble remembering Claire Temple.
"The plastic tips at the end of shoelaces are called aglets. Their true purpose is sinister."

immediately after JJ season 1 finale

Death is the road to awe.

This show takes place after JJ.