I think the missing flag is:
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': OMAN, MANITOBA, ROMANIA, CAYMAN ISLANDS.
2. Places which have chemical elements named after them: FRANCE (Francium and Gallium), POLAND (Polonium), JAPAN (Nihonium), TENNESSEE (Tennessine).
3. Places whose names contain a 4-letter word in English: BOTSWANA, BARBADOS, FINLAND, DENMARK.
4. Flags with horizontal stripes in the design: ANGOLA (2), GABON (3), KENYA (5), EGYPT (3).
A flag which therefore satisfies all 4 of these groups is:
Germany's, since (i) GERMANY contains 'MAN', (ii) the element Germanium is named after Germany, (iii) GERMANY contains both 'GERM' and 'MANY', and (iv) it includes 3 horizontal stripes in its design.