One thing you have to consider is which part of the Amazon. Conditions in Peru at a particular time might be different than conditions in Brazil at the same time because the areas can be far apart. Since the area is so close to the equator, the temperature does not very much thoughout the year. The rainy season in the Peruvian Andes starts in about December and is heaviest in the Iquitos area in April. In the Manaus area, the rainy season is roughly mid-December till mid-May. In Ecuador, April to August is the rainy season (able to see more monkeys and birds), while August – March is the dry season (more mammals than birds).
Water levels traditionally peak in the Iquitos area at the end of April (also fed by melting snow from the Andes), while they peak in the Tefe Brazil area around June or July. The river levels can vary by about 50 feet between low and high water seasons. The area around Manu National Park and the Tambopata Reserve are not affected quite as much, though they did have problems getting to the Heath River Lodge a few years ago.
But going in the rainy season can have it's advantages. Since most riverine plants fruit and flower during this period, it is one of the best times to see birds and monkeys at the waters edge. It is also good for canoeing and kayaking. Around the Amazonia lodges, it is also the best time to see dolphins and tree frogs
The dry/low water season is best for hiking, camping and fishing. For example at the Amazonia lodges, the peak season for extended hiking is normally about July-November