Merhaba, 

In the Turkish Airlines commercial, it said "Bu Gurur Turkiyenin" which means: This is the pride of Turkey

Shouldn´t it be "Bu Turkiyenin Gururu"? 

Are both correct? 

Then what about "End of the World" in Turkish?

Dunyanin Sonu 

or

Son Dunyanin

or both correct?

Teşekkurler

Look at the positions of commas:

Bu gurur, Türkiye´nin  "This honor belongs to Turkey"

Bu, Türkiye´nin gururu "This is Turkey´s honor."

Dünyanın sonu "The end of the world"

Sonu dünyanın Word order is wrong. This can be only poetic. Not acceptable in written and daily speech.

Just a little addition: my experience is the word order can mislead you but possessive structures usually don´t. In this case gurur cannot be connected to Türkiye´nin because if it was it would be marked with the possessive suffix.

Not necessarily!

benim kız-ım = my daughter/girlfriend

benim kız = my daughter/girlfriend (possessive dropped, genitive left)

I would say:

Bu gurur Türkiyenin = This pride is Turkia´s

Türkiyenin gururu = Turkia´s pride