Number 1, does he have kids?  How many?  How old?  Where do they live, ie who has custody?  If they visit, how often?  When?  Is that a regular schefule or "whenever"? 

If they live with him, full stop.  (Start thinking about your exit.) Why do they live with him, ie, is BM unstable?  If they live with him due to BM's instability, another full stop. (Really consider exiting.)

If you've gotten this far, you've probably met the kids.  Are they well-behaved and clean?   What does your gut say?  Check out his housing, does it seem suitable?   As you get to know him more, see if he's "done the work", ie,  realistic legalities, workable relationship with BM, paying child support on time, planning ahead like summer care, etc.

In your case with older BF and older kids, I'd want to know ALL about launch plans.  I'd be especially watchful to see if either or both girls are mini-wives.  

Good luck and keep your eyes open.

Adding:  Whatever you hear about launch plans, look for evidence it's happening, like college attendance (regular), jobs, boyfriends.  If you dont see that concrete evidence, run unless you choose to live with one or both of these girls.

What a great question. I agree with JRI's suggestions. I'd also watch and observe. What some people say (outside of the obvious facts) and how they act are two different things. 

 Aside from DH letting on like everything was perfect, he seemed uncomfortable around me when his phone would ring and it would be the kids or the ex (calls always came Fridays around dinner time/Friday night date time). When he'd go to see the kids for a weekend, his calls to me were sparse even though we were talking regularly/daily (I expected him to have uninterrupted time with his kids, but even his calls to say hi, I'm alive, or to touch base were hurried and sounded hushed/hidden).   

Later on, he was very slow about introducing me to the kids. I mean VERY slow. And the big honking blaring red flag was that visits to him were stopped after BM learned we were dating. Suddenly, the CO was no longer followed and the kids had a boatload of activities every weekend and all summer--for three years! Of course, they were always free if he could head that way for visits.  

What I missed/chose not to see early on: He had an ex who was NOT ok with him getting involved with anyone, and she passed that displeasure and insecurity onto the kids (ultimately, presenting it all as abandonment). He feared what his ex would do if/when she found out he was dating again (oh, and we found out!). He was like a puppet back in those days. It took me a long time to see it all for what it really was. And it took a long time for him to cut the puppet strings. 

Do you have kids at home?

Yes.

Full stop.

KISS

Does your BF treat you differently when his kids are around? (From not holding hands to completely ignoring you?). Does he say "I" instead of "we" when talking about an activity you and he have done? Does he ever say no to his kids? Does he cancel plans with you to do something with/for his kids? Does he answer his phone when his kids call, no matter what you're doing?  Does he share personal things about you, or about you as a couple, that should be private? Does he spend more money than he has?

Thats a good start. 

My SO had significant issues with shyness with women and, still being single and without sex life to mention at almost 30 married a woman that finally showed interest in him and offered a promise of company and regular sex. Without any dating experience,  HE ignored all the red flags, like every single person in her immediate family had a severe genetic disorder resulting in a physical or mental disorder, including severe mental retardation and incurable disorders that have life expectancy of three decades max (her). 
 

These flags should have been my flags too, as while she carked it years before I came on the scene, her kids 1. are severely traumatised from basically being abandoned by her as babies (she would only spend a few hours during the day with them as her health always was more important), then witnessing her awful, slow, protracted end as toddlers, 2. Inherited a diluted version of her family's disorders and have significant behavioural issues that go with that, plus they'll have to get genetic tests done when it's their time to reproduce, as if their future partner has them too, they'll birth children doomed to slow and cruel death at the end of short life 3. take it all out on their father, because mother can be idolised, as an absent parent, dead or estranged.

I am child free, and I should have looked for a man who's child free too. I love my SO, he's very kind to me and others, we have intellectually stimulating conversations, intimacy is also like with no one else I've been with before, but the children part is pure hell. I don't mind them, each one, when I get them one to one is lovely, but together they're Satan's spawn - constant aggression towards each other, their father, they're destructive just for fun and wreck everything they breathe on, expect entertainment and dad to spend money on them every minute they're not at school. I don't love them and don't think I ever will, but would be happy to be proven wrong with this. I don't think anyone can love a child "as their own", when it's not their own, which is another reason I find their mother's decision to birth them (via IVF, nonetheless) when she was clearly on her way out so horrifically selfish. They seem to have a better relationship with me than with their father though, and some days are fine, but now I find myself hypervigilant around them. They're embarrassing to be with out in public, always insisting on wearing stained, torn sportswear only and eat like wild animals. They don't even own  shoes that aren't from a sports shop or a pair of jeans, because that'd be "too fancy". Mind you, my SO are in well paying, conservative professions and would be more than happy to dress them well. They have no shame about having a physical fight in a nice restaurant and are completely self centred. They're tweens/early teens, mind you, and excel academically and athletically. 
 

I have said to my SO, that if things ever ended between us, I just won't bother dating again. It's too much stress, and if I ever ended up in a relationship again, it would have to be with a man who'd have to come and find me at home. Maybe a door to door salesman or a plumber. I don't give a hoot anymore. I dated enough abusive, exploitative men, and this one is really nothing like my previous ones, but still with a massive baggage. Luckily, we don't live together and I've locked in a weekend for just us,  without the spawn every month.

red flags a'plenty.

Went back to your previous post. Oh boy!

He did you an enormous favor. Stay away from guys:

~ Kids older than 18 living with him full time, especially daughters. Read up on "miniwife syndrome".

~ Whats the relationship with bio mother, whats she like? Are they enmeshed and she calls texts several times during the day. Has she weaponized the children/skids?