I think the missing flag is:

>! [![enter image description here][1]][1]  
>!  
>! i.e. the flag of **GERMANY**

The flags depicted are (left to right, top to bottom):

>! ANGOLA, OMAN, MANITOBA, FINLAND;  
>! KENYA, ROMANIA, DENMARK, FRANCE;  
>! POLAND, CAYMAN ISLANDS, GABON, EGYPT;  
>! JAPAN, BARBADOS, BOTSWANA, TENNESSEE.

The four connecting groups are:

>! 1. **Places containing 'MAN':** O**MAN**, **MAN**ITOBA, RO**MAN**IA, CAY**MAN** ISLANDS.  
>!  
>! 2. **Places which have chemical elements named after them:** FRANCE (Francium and Gallium), POLAND (Polonium), JAPAN (Nihonium), TENNESSEE (Tennessine).  
>!  
>! 3. **Flags with a horizontal black stripe in the design:** ANGOLA, KENYA, EGYPT, BOTSWANA. (Prompted by @JeremyDover in comments)  
>!  
>! 4. **Countries with a female leader:** FINLAND ([Sanna Marin](https://en.wikipedia.org/wiki/Sanna_Marin), PM), DENMARK ([Mette Frederiksen](https://en.wikipedia.org/wiki/Mette_Frederiksen), PM), GABON ([Rose Raponda](https://en.wikipedia.org/wiki/Rose_Christiane_Raponda), PM), BARBADOS ([Mia Mottley](https://en.wikipedia.org/wiki/Mia_Mottley), PM).

A flag which therefore satisfies all 4 of these groups is:

>! Germany's, since (i) GER**MAN**Y contains 'MAN', (ii) the element Germanium is named after Germany, (iii) it includes a black horizontal stripe in its design, and (iv) the current (female) Chancellor of Germany is [Angela Merkel](https://en.wikipedia.org/wiki/Angela_Merkel).

<sub>Note:</sub>

>! <sub>I suspect the prominent mention of "*right now* (and that’s important to remember!)" in the flavour text is an indication that something related to **current affairs** (and which may change in the future) is key to the puzzle. With the fourth category focused on **politics** (where leaders may change in elections) I think this hidden hint is satisfied.</sub>

  [1]: https://i.sstatic.net/0BmnE.png