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Where can I get Trompenaars' country level culture scores?

You'd probably have to contact Fons Trompenaars directly.

The "country-level scores", similar to those provided by Hofstede or GLOBE, in their complete form have not been published; at least not in any of Trompenaars and his associates' publications.

Rather than providing composite scores for each of the dimensions, Trompenaars and his co-authors normally provide item/scenario scores. The list of scenarios changes from publication to publication. For example, for Universalism-Particularism, the "car and pedestrian" scenario is mentioned in every publication, but in some publications other scenarios are also mentioned ("restaurant review" and/or "insider trading" and/or "insurance fraud"). It is not clear how many scenarios were used to measure each dimension, how the composite scores were calculated, and whether or not the composite scores were calculated at all.

Some critics point out that depending on the scenario the country rankings can change substantially, which raises questions about reliability of the measures and validity of the composite scores, if such exist. Unfortunately, no reliability and measure structure data are reported in Trompenaars and his co-authors' books.

Also keep in  mind that if you choose to use the country item scores provided by Trompenaars, they do not represent the level of agreement with or degree of internalization of certain values (e.g., on a 1-7 scale), as would be the case for Hofstede's or GLOBE's indices, but rather the % of the respondents who agreed or disagreed with a statement. As you understand, such data may violate the "normality" assumptions of OLS and related methods and may need to be analyzed using other techniques.  

In conclusion, I personally am a big fan of Trompenaars' model and believe that conceptually it may be the best one out there. But the lack of quantitative information about the model and measures makes it impossible to use it in research. Hopefully, more information will be released someday.

For more on the topic see:

Hampden-Turner, C., & Trompenaars, F. (1993). The Seven Cultures of Capitalism: Value Systems for Creating Wealth.

Hampden-Turner, C., & Trompenaars, F. (2000). Building Cross-Cultural Competence: How to Create Wealth from Conflicting Values. New Haven & London: Yale University Press.

Trompenaars, F. (1993). Riding the Waves of Culture: Understanding Diversity in Global Business. Chicago, IL: Irwin Professional Publishing.

Trompenaars, F. (2003). Did the Pedestrian Die?: Insights From the World's Greatest Culture Guru. Oxford, UK: Capstone.

Trompenaars, F., & Hampden-Turner, C. (2004). Managing People Across Cultures (Culture for Business Series): Capstone.

Trompenaars, F., & Hampden-Turner, C. (2012). Riding the Waves of Culture: Understanding Diversity in Global Business (3 ed.). New York, NY: McGraw Hill.

Trompenaars, F., & Woolliams, P. (1999). Trans-Cultural Competence. U.K.: People Management.

Trompenaars, F., & Woolliams, P. (2003). A new framework for managing change across cultures. Journal of Change Management, 3(4), 361.

Where can I get Trompenaars' country level culture scores?