Hello Mike
No the short term arrangements in response to life events (unpredictable, ad-hoc, relatively short term), wouldn't be captured within the legislation governing flexible working, as that legislation is intended to offer a route by which an employee can make a request to vary their terms & conditions in order to work differently (e.g reducing hours, changing work pattern - if work pattern is contractual, etc); as it currently stands, the legislation provides for the change to ts & cs to be permanent (although many orgs choose to expand this and offer temporary changes if it works for the parties). Time off for the areas you describe would broadly fall under 'other absence' (e.g medical appointments, probably under your sick leave/pay policy, in terms of how the time off for appointment is recorded/remunerated etc), compassionate leave (no current legislation governing this in broad terms, so up to employer to decide what it offers ie how long, whether paid/unpaid or combination etc, )
Would suggest keeping 'absence types' of leave outside of Flex working, as flex working is about how people can work in their jobs, and the former is about provisions for short,unexpected periods of leave (mainly non-repeating in terms of compassionate leave eg. for funerals/bereavements etc).
Hope this helps
ann

Tanks Ann On reflection, I thought this would be the case. Thank you for confirming what I should have seen as obvious. I just assumed short-term arrangements may have strayed into the legislation. Thanks again for your feedback. Mike