TrumpScript, 938 bytes

As always nothing is, 1000001 minus 1000000;
And Putin is, 1000003 minus 1000000; great
Just as Trump is, 1000005 minus 1000000; even better
Also as America is, Putin times Trump; the best
Most importantly Ivanka is, 1000101 minus 1000000;
And believe me that Hillary is nothing
As long as, Hillary thinks less of Ivanka;:
China is friends with Hillary
Democrats are idiots like Hillary
Obama is in line with Hillary
As long as, China thinks its more than America;:
Make China, China minus America;!
As long as, Democrats fear more Trump;:
Make Democrats, Democrats minus Trump;!
As long as, Obama gets more arsenal against Putin;:
Make Obama, Obama minus Putin;!
If everybody thinks, America is China?;:
Say "FizzBuzz"!
Otherwise: if we ask, Democrats are Trump?;:
Say "Buzz"!
Otherwise: what if, Obama is Putin?;:
Say "Fizz"!
Otherwise do this: tell Hillary all her lies!!!
Hillary is, as always Hillary plus nothing;!
America is great.

Try it online!

I was quite bored... Not too efficient, but fun!

TrumpScript, 938 bytes

As always nothing is, 1000001 minus 1000000;
And Putin is, 1000003 minus 1000000; great
Just as Trump is, 1000005 minus 1000000; even better
Also as America is, Putin times Trump; the best
Most importantly Ivanka is, 1000101 minus 1000000;
And believe me that Hillary is nothing
As long as, Hillary thinks less of Ivanka;:
China is friends with Hillary
Democrats are idiots like Hillary
Obama is in line with Hillary
As long as, China thinks its more than America;:
Make China, China minus America;!
As long as, Democrats fear more Trump;:
Make Democrats, Democrats minus Trump;!
As long as, Obama gets more arsenal against Putin;:
Make Obama, Obama minus Putin;!
If everybody thinks, America is China?;:
Say "FizzBuzz"!
Otherwise: if we ask, Democrats are Trump?;:
Say "Buzz"!
Otherwise: what if, Obama is Putin?;:
Say "Fizz"!
Otherwise do this: tell Hillary all her lies!!!
Hillary is, as always Hillary plus nothing;!
America is great.

Try it online!

I was quite bored... Not too efficient, but fun!

Pseudocode:

var nothing = 1, Putin = 3, Trump = 5, America = Putin * Trump, Ivanka = 101, Hillary = nothing;
while Hillary < Ivanka
 var China = Democrats = Obama = Hillary;
 while China > America
 China = China - America;
 while Democrats > Trump
 Democrats = Democrats - Trump;
 while Obama > Putin
 Obama = Obama - Putin;
 if China == America
 print "FizzBuzz";
 else if Democrats == Trump
 print "Buzz";
 else if Obama == Putin
 print "Fizz";
 else
 print Hillary;
 Hillary = Hillary + nothing;
America is great.