A creature like this is barely possible.
A bird usually needs between 1/4 and 1/2 of it's body weight in food to live each day. As we will be talking chitinous insects and an active lifestyle, lets use the upper end of that spectrum.
Lets say that allows the bird to fly 1/8th of each day which means the birds is small and its flight is supported by environmental conditions so the flying is easy. This seems high as I am envisioning a house sparrow as the control. With flying creatures smaller=easier.
Using a very rough average sparrow: it is about 30g and has a cross sectional area of about 17 square cm. As it needs to catch its food, lets optimistically say that its feathers collect all food it touches and it picks the food from its feathers while perched. For fun lets use the average airspeed velocity of an unladen European swallow which seems to be about 11 meters per second.
Using these assumptions which for actual science are insufficient, the bird would need to fly through air with an average food concentration of .075g/m^3 of air. If the bird only ate gnats, that would be on average 75 gnats for every cube meter or it would have to catch an eat a gnat every 1/8th of meter it flies. That is 88 gnats a second.
Why do I think that is still possible? I am going to assume the bird eats pollen, spores, or floating insects which cannot avoid it; while resting/picking its feathers it is still able to catch food by positioning itself in a windy area; and it opens its wings to maximize its catching ability. As we are describing an ideal environment for such a creature and it needs a lot less food as it would fly a lot less, it is possible that such a creature could evolve to take advantage of this described niche.
Please note, however, that any such creature is highly dependent on its environment. Most seem like they would be willing to catch larger insects or pick up food on the ground if available. It would also be high susceptible to hazards such a predators or environment contamination. This works well in water as its buoyancy allow it to hold a higher food concentration that air can. It is fun to dream of a giant bird which flies efficiently all the time by gliding everywhere. At the elevations where gliding is possible, however, it would not make sense to me for there to be enough food.