What is the convention for use of "volume" or "amount" in reference to quantity of data?

As already stated in the comments, both are perfectly fine. While some people may report that they detect some nuanced difference in meaning, these perceptions vary from person to person (as evidenced e.g. by the comments to your question). Therefore, usually these two terms can be used as synonyms.

Examples of use in published literature written by native speakers

In the following entries, the two are clearly treated as synonyms:

Volume of data stored – The amount of data stored is a key driver for the database platform required.

^{From David Haertzen, The Analytical Puzzle Data Warehousing, Business Intelligence and Analytics, 2012. (link)}

This would add unnecessary complexity to the database and vastly increase the amount of data to be manipulated and stored. Indeed , management of such a volume of data would probably be beyond the present capacity of most GISs…

^{From Simon Fitch, Vincent L. Gaffney, and Kenneth Thomson, 'Merging technologies: Integration and visualisation of spatial data', in Mapping Doggerland: The Mesolithic Landscapes of the Southern North Sea, Kenneth Thomson, Simon Fitch, and Vincent L. Gaffney, eds., 2007. (link)}

Technically, the amount of data that can be stored by traditional databases is unlimited. However, the greater the volume of data being collected and shared, the more difficult mining, fusing, and effectively using…

^{From Isaac R. III Porche, Bradley Wilson, Erin-Elizabeth Johnson, Shane Tierney, and Evan Saltzman, Data Flood: Helping the Navy Address the Rising Tide of Sensor Information, 2014. (link)}

Many other examples can be found if one searches google books with the two search terms

"volume of data" "amount of data"

(like this).

The relevant dictionary definition

As far as the dictionaries, the Oxford English Dictionary (OED) lists the following as one of the meanings of the word volume:

7.b. The amount or quantity of something.

1882 D. A. Wells Our Merchant Marine 112

So small a matter apparently as the civility or neglect of conductors..will sensibly influence the volume of travel.

1886 Manch. Examiner 13 Mar. 5/2

It would be a good thing to enlarge the volume of the currency; to make money more plentiful.

1892 Daily News 24 Dec. 7/2

The volume of business, as is usual at this season of the year, has undergone considerable diminution.

In other words, the OED says that when volume appears in the construction volume of something, then volume just means amount or quantity.

Frequency of usage

Having said all that, Google Books Ngram Viewer indicates that amount of data is these days about five times more common than volume of data:

Similarly, in the Corpus of Contemporary American English (COCA), we find 618 hits for amount of data and 86 hits for volume of data (so their frequencies differ by a factor of 7 in COCA).

Final note

Obviously, if a particular author decided to use either of these two terms in some narrower sense such that the two aren't synonymous, that's perfectly fine, as long as the author provides a clear definition and uses the terms consistently. But unless such a special differentiation is clearly explained, one should in fact assume that the terms are synonyms (as they are in the examples provided above).