Not sure about aggregated data, but in the United States registered "non-profit" organizations, including wildlife conservation organizations, make their financial reports available to the public. You can either search in the organization's website, or use websites run by watch-dog groups (there are quite many of them). However, this applies only to those registered with the government as "non-profit" for tax exemption purposes. For others you won't know how much donations they get. I suspect you can find similar resources for some other countries.
Watch dog groups often publish annual overview of charity donations but not necessarily with a break down of the different categories (e.g. wild life, health, religion, etc. etc.)
I would suggest you have a look at the UK's Environmental Grants Network - they publish a report called 'Where the Green Grants Went' - their latest one is version 6. If I'm not mistaken, it gives a total philanthropic spend in the UK. There are similar networks in other countries (Australia, Europe, US, Canada) and they may have similar statistics. It won't give you a global figure, but it will give you a good idea of a minimum
"Charity Navigator" keeps track of numerous nonprofits and they provide the necessary summary information. They provide an independent assessment of accountability and effectiveness. They would be a good place to start.
It is indeed surprising how little of this is available. Amongst the few studies that I am aware of is the one of Katherne Scholfield and Dan Brockington on spending of (international) NGOs in Africa (years 2004-6), A good introduction to their work is
Brockington, D., and K. Scholfield. 2010 Expenditure by conservation
nongovernmental organizations in sub-Saharan Africa. Conservation
Not sure about the answer to the question, but just to complicate matters volunteer surveyors contributed the equivalent of 1.7 million hours of their time each year (equivalent to around 1 000 full-time staff) monitoring Britain's bird populations for BTO (http://www.bto.org/volunteer-surveys) which is valued at something like £35 million (or US$60 million)
I'm not sure about the total value of donations that question but I think the value that the pubic organizations such as governments aimed at conservation can be extracted from the GDP numbers. Is that part of public expenditure that governments allocate for its annual management aimed at conserving biodiversity.