Yes, you can export Alexa's Site Keywords, Keyword Difficulty, and Competitor Keyword Matrix data.
To export Site Keywords
- Go to https://www.alexa.com/pro/keywords/site.
- Enter a site URL.
- Click the Download icon at the top of the table.
You can also export paid and paid competition keywords.
To export Keyword Difficulty lists
- Go to http://www.alexa.com/pro/kwopportunities.
- Enter a query.
- Set the filters so that the list returns the keywords you care about most.
- Click the Download icon at the top of the table.
To export Competitor Keyword Matrix lists
- Go to https://www.alexa.com/pro/keyword-matrix.
- Enter a single site, list of sites, or use a saved site list.
- Click the Download icon at the top of the table.
Note that all keyword exports are limited to 1,000 lines.