What caused the Nazis to use the Swastika as their symbol?

This is the answer according to Brewers Dictionary of Phrase and Fable.
The 'Gammadion or Fylflot',an elaborate cross-shaped design used as a charm to ward off evil and bring good luck.It was adopted by Hitler as the Nazi emblem about 1920,probably from the German Baltic Corps,who wore it on their helmets after service in Finland,where it was used as a distinguishing mark on Finnish aeroplanes. It is from the Sanskrit 'svasti',meaning 'good fortune'.

You can find out from the Fuehrer himself. The following site, which is not offensive, quotes from Mein Kampf in an effort to answer this question precisely.

The organization of our monitor troop clarified a very important question. Up till then the movement had no party insignia and no party flag. The absence of such symbols not only had momentary disadvantages, but was intolerable for the future...party comrades lacked any outward sign of their common bond...[Hitler then writes about how he attended a mass Marxist demonstration:] a sea of red flags, red scarves, and red flowers...
I have, in our movement, always upheld the standpoint that it is a true good fortune for the German nation to have lost the old flag...from the bottom of our hearts we should thank Fate for having been gracious enough to preserve the most glorious war flag of all time from being used as a bedsheet for the most shameful prostitution. The present-day Reich, which sells itself and its citizens, must never be permitted to fly the black, white and red flag of honour and heroes...

The question of the new flag - that is, its appearance - occupied us intensely in those days. From all sides came suggestions...the new flag had to be equally a symbol of our own struggle, since on the other hand it was expected also to be highly effective as a poster...an effective insignia can in hundreds of thousands of cases give the first impetus towards interest in a movement. For this reason we had to reject all suggestions of identifying our movement through a white flag with the old state...white is not a stirring colour. It is suitable for chaste virgins' clubs, but not for world-changing movements in a revolutionary epoch. [other assessments of various colours also]

I myself always came out for the retention of the old colours, not only because as a soldier they are to me the holiest thing I know...nevertheless, I was obliged to reject without exception the numerous designs which poured in...which for the most part had drawn the swastika into the old flag. I myself, meanwhile, after innumerable attempts, had laid down a final form; a flag with a red background, a white disk, and a black swastika in the middle. After long trials I also found a definite proportion between the size of the flag and the size of the white disk, as well as the shape and thickness of the swastika.

https://www.crwflags.com/fotw/flags/de%7Dns_or.html#ori

The swastika used to be a very common symbol. It was a often a good-luck symbol. The Girls' Club of America used to have a magazine called 'The Swastika.' The Boy Scouts gave out a swastika badge up until 1940. The footprints of the Buddha were said to be Swastikas. There was an interesting magazine article I saw a few years ago with LOTS of pre-Nazi swastika emblems. It was just a common symbol.

http://mentalfloss.com/article/57165/why-did-nazis-hijack-swastika

Well first, HItler grew up literally with the swastika,it was like his symbol.And second,Hitler loooooved history(like me)and the swastika ment good luck,and finaly the early peoples such as the Romans used it and Hitler took a lot from the Romans.