They don't, but employers don't know that. In the eyes of the law they are women, and it's not for employers to dispute this. Who's going to argue that they don't get periods without being accused of discrimination?
Oh, i genuinely thought your original comment was a joke.
If they are flexi, doesn't matter the reason for swapping days, as the company has okayed them.
If they want to take a sick day due to being unwell regardless of periods pains or not, whether they have them or not, then it is no different from being ill normally. There is nothing stopping these people from claiming flu every month but then they would have to face scrutiny of the employer. If the employer thinks that you are taking too much time off, they can request that you get some sort of document or notice from a doctor. You can comply and be found out that you pretended that you had a uterus or you can argue all sorts of things and eventually be caught out.
If you suffer from a condition that could significantly effect work and the employer asks you about it during recruitment or when signing HR documents, then you must say so if you wish to receive special treatment accordingly. Employers at this point can ask for medical notice as proof to accommodate your needs.
Your point can be applied to literately any illness/sickness/re-occuring injury and does not have to be in the context of a trans pretending to have periods.
Try having endometriosis and then having to function. A lot of women have gynae issues such as this, but get fobbed off by GP's for years and years because they say it's "just" their period and they should accept it because they're a woman.
These women are well within their right to seek another professional to assess them, another woman if they feel that they can empathise better and more accurately judge the severity. I know several women who have prescription medication to deal with these pains and although i don't doubt at all there is discrimination in some cases, the severity of pain is subjective and the doctors try to make a judgement based on a number of things such as long term effects of taking heavy medication, possible addiction to these medicines. You cant hand out meds to everyone who thinks they need it and in some of these cases they are not given strong prescription drugs because they believe it is in the best interest of the patient.