I've done extensive research on chaingrabbing fox and falco, and most of my percents are confirmed with m2k. Also note that all of these percents are before the actual throw does any damage.
Technically, you can start the chaingrab as low as like 18% on fox, and falco would be around 23% cuz he falls a bit faster. This means that if fox fully DI's to either side of you, you can still regrab him once he hits 18%. However, this is playing frame perfect and probably can't be done without AR. Most people can't do a successful chaingrab til after 30%.
The chaingrab is than impossible to escape, no matter how they DI. If they stop DI'ing, and jump out as soon as the "hitstun" of the grab wears off, they can jump out at about 108% (fox) or ~114% (falco). However, this is only if you are grabbing them perfectly so that you are grabbing them as soon as they enter your grab range. Due to human error, most people end up being able to jump out a bit sooner.
I personally stop chaingrabbing Fox if he is over ~104%, and I stop chaingrabbing falco if he is over 108%. Remember that people don't jump out frame perfect, so even if your not perfect, they won't always jump out properly.
If Fox and Falco do not stop DI'ing fully left or right, you can keep regrabbing them 145%+ percent. I believe it even goes well over 150% if you are frame perfect, but I always stop at 140 cuz I just nair after that. Note that if they only slight DI, they will be able to jump out sooner, depending on how slight the DI is. Not that you can really be sure, but as a general rule, I would say that slight DI will allow them to jump out between 118%-130%ish depending on how slight that DI is.
(Note- The following information about falcon is less based on research, and more based on experience through gameplay, so the percents may be plus or minus 5%.)
With Falcon you can do the same thing as fox and Falco, only the chaingrab starts sooner, and ends sooner. Falcon cg starts at 0%, and goes til ~74% if they stop DI'ing. I would stop cg'ing them after 70. If they keep full DI'ing left and right, they can't jump out til 94~.