The most common preposition used with "prices" is "of", but "for" is sometimes used as this ngram shows.
I would suggest that "prices for" is only really appropriate if there is some human element, because the word carries purpose or belonging. For example:
The shopkeeper is introducing new prices for his customers.
To me, "for" does not sound correct in your example, and that is probably because there is no person involved. I would definitely express it as:
Prices of gasoline have been fluctuating all month.
You may also note that the ngram above shows much less frequent use for the plural of "price". That is because it is more common to speak of one price because multiple identical items have the same price. However in your example it may well be correct to use the plural because the same fuel is often offered at different prices in different places, so when speaking blanketly about fuel costs over the country it seems correct to say "prices".