We usually say "flying north". If you wish to use "north" as a noun (as an object to a preposition, for example), we need the definite article: "flying to the north." This construction, is less common, and also a bit ambiguous, since it's not clear if "to the north" is a direction of travel or a location relative to the speaker. The phrase "flying northwards" indicates direction of travel, but unlike the other two phrases, does not suggest arrival in a location that would be termed "the north".

North is a direction, not a place. They are flying north, works because 'north' functions as an adverb to modify the verb 'flying' indicating the direction of the verb. It doesn't work as an object of the prepsotion 'to north' because even though it can be used as a noun, it is not an object, it is a direction. You could however say northward.

We cannot say flying to north as in this sentence the word north is a noun - if you wanted to use “to” then your sentence would need to be “ the birds are flying to the north” remember the word north can be a noun , adjective or an adverb

What about "Birds are flying toward/s north" ? Do these two sentences mnmean the same? 1)I run to the park 2)I run toward/s the park