First trees originated in Devonian age (416‐359 Ma). The higher diversity originates to the time of the Carboniferous Forests (360‐300 Ma). I think the origin of the tropical forests is the same, so you need to define the starting point for each tropical area to compare the ages.

Citation:

Morley RJ (2000) Origin and evolution of tropical rain forests. Wiley, Chichester ; New York.

Keep in mind that the presence of a habitat which can be classified as rainforest at a given time does not mean that the rainforest tree lineages present there currently were already in place. They may have in the meantime colonised from other regions or from other types of environments. Tree lineage persistence would depend on how constantly humid the climate in the region may have been around the year or over millions of years, how the size of the rainforest-covered region may have fluctuated etc. If there were substantial changes, rainforest may be present in the same place as it was a hundred-odd million years ago, but with a very high turnover in tree lineages. So, depending on what you are trying to get to, the time when rainforest first appeared in a region may not be very relevant.

Firstly you must ask, what do you mean by 'tropical forests' I call tropical forests 'megathermal forests' as their present day restriction to the tropics is an artefact of living in an interglacial during the Quaternary, when the limit of frosts in areas of wet climate approximately coincide with the tropics of Capricorn and Cancer. In glacials, this boundary was more equatorward and in the Eocene thermal maximum and also at other times during the Cenozoic much more poleward. Then, are you thinking of rain forests, or forests with a closed canopy? My understanding is that it is the development of a closed canopy which makes rain forests so special and different from other forests. The closed canopy creates a special microclimate and additional niches which help make megathermal rain forests such a harbour for the establishment of new species. My understanding is that such forests first appeared in Western Gondwana (areas such as Gabon or Brazil) in the Late Cretaceous, sometime during the Campanian (84-74 Ma) and then in India as it drifted into the equatorial zone. In N America, they appeared during the Paleocene, and in SE Asia, probably also became established well after their initial appearance in W Gondwana, explaining the low level of origination of angiosperm families in the Southeast Asian region.

Thank you everyone for informative and impressive answers.

Given that many tree species in the tropical rainforests are angiosperms (flowering plants) they are not as old as "plants" in general (i.e Devonian).  It is understood that angiosperms became prevalent in the geologic record from the mid-Cretaceous on.  much of Sub-Saharan Africa (Atlantic margin) has been at the same or very similar latitude since the Early Cretaceous, as has Brazil.  However, as Mr Morley points out, the latitudinal extent of the climate conditions that allow for tropical rainforests is modified during periods of climate change.  For example, the Sahara itself was green with flowing water ~ 8,000 yrs ago.  The mid to late Cretaceous was a dominantly greenhouse period, especially the Cenomanian-Turonian.  Greenhouse periods are typically characterized by higher water vapor in the atmosphere (more humid), which allows for the expansion of these types of environments.  On the other hand, grasslands evolved in the Miocene.  The global expansion of those plants actually resulted in a decrease in surface moisture, which detrimentally impacts the forests.  The process is called precipitation recycling, and it is an important factor in the sustainability of a forest environment.  The location of topography also has a strong effect on the latitudinal movement of jet streams.  The global topography has changed significantly since the mid-Cretaceous, such that the specific location of rain belts has also been modified since then.

I have not seen any published work specifically comparing the age of the tropical rainforests in the Congo, Amazon and Asia.  If you mean the actual age, as in the oldest plants currently living, then that research would be in the biology/ecology realm.  If you mean the age of the environment, then looking at the palynology & paleoclimate literature is your best bet.  Soil science work could be useful, but these soils are leached pretty effectively, so that may only give you  a minimum age.