If OP and her partner decide to keep the affair secret, then I don't see how they can say they are BF/GF. They are not in a real life relationship. If they continue believe they are putting the emotional needs of their ex wives and husbands before their own desire to be together then they are just 2 people who are still having an affair.
How long should they keep this secret going? 3 months, 6 months, a year? I am cynical, if my sister ditched her husband and 3 months or even 6 months later found her 'soul mate' who just happened to be recently divorced and was someone who was an acquaintenance before they split. I would put 2+2 together and assume 'affair' and get it right.
I doubt many women who leave a bad marriage suddenly end up in another relationship so quickly, they tend to want to enjoy the single life, get their kids settled and not rush into another bad relationship.
I would have thought a year would be minimum.
I also think its pretty shit to pretend to be single whilst going through a financial settlement as I said upthread DH could have pretended I didn't exist (not an OW before I get flamed) so he could get a greater share of the marital assets in order for his own housing needs to be met (the size of the mesher charge). So your partner's poor ex is coming to terms with being a single mum, the breakdown of her marriage, and she's got to try and get a fair settlement for herself and the kids without knowing all the facts.
I bet when your partner decides its time to finally start this relationship, you'll only be seeing each other 3 nights a week, and he won't be spending any money on romantic weekends because his ex will be going through his finances with a tooth comb.
So what then? You are going to wait until the settlement is over? And continue to have your emotional needs placed below his ex wife.
Then you've got the kids to think about. His kids will hate you because you aren't their mum and your kids will hate him because he's not their dad. Blending that family has got to be taken very slowly. So if you wait one year before you can even pretend you've been on one date, you've got to wait another 6 months to a year before you introduce the kids, and maybe another 6 months before he moves in.
so really to move from being OW which you still are to the girlfriend you want to be is going to take over a year especially if you want it to look like you are both 'innocent'.
I don't begrudge you a relationship with this man, but have you thought about the practicalities involved?