There are three strategies that you can follow.
The first strategy is to express these variables in terms of nominal GDP for which the WDI provides the current US$ values. This will not give you constant price numbers of course but it will provide you with a number that is not influenced by inflation as both the numerator and the denominator are influenced in the same way by inflation. The proper interpretation of a series in per cent of GDP is that it reflects the importance of the flow for the economy. (If the economy grows and all else remains equal the ratio of flow to GDP decreases).
The second strategy is to divide the series in current US$ by an appropriate deflator (index number). Here you have to chose an appropriate indicator, for example, the US Consumer Price Index and the US GDP deflator. You can get the US CPI from the WDI (current base year 2005 = 100). (The US GDP deflator could be used in the same way; the WDI provides annual percentage changes - so the inflation rates - that you should use to calculate the indexnumbers). Deviding the current US$ values by the index numbers will provide you with a constant price series in 2005 US prices. This corrects for US inflation but in some cases that may not be what you need.
The third strategy is to express the series in another currency and then use the appropriate price index number related to that country. For example if you want to know how much goods and services could be bought by the foreign finance flow to which the question refers in the recipient country the you should use the local currency unit. This recipe requires two steps
- Use the WDI DEC alternative conversion factor LCU per US$ (The DEC alternative conversion factor is the underlying annual exchange rate used for the World Bank Atlas method. As a rule, it is the official exchange rate reported in the IMF's International Financial Statistics (line rf). Exceptions arise where further refinements are made by World Bank staff. It is expressed in local currency units per U.S. dollar.)
- Divide the LCU value by the country CPI index (the base year will differ by country)
Book: Section 3.2 pp. 29-33.