There's a few reasons why a tomato plant won't flower.
When temperatures rise above 85 to 90 degrees F (depending on humidity) during the day and 75 degrees F at night, pollen will become unviable. Humidity can also come into play. In the extreme humid regions of the U.S., pollen may become so sticky that it does not fall.
On the other end of the spectrum, in the arid regions, pollen may become so dry that it does not stick to the female part of the flower. Many gardeners try to gently shake the plant to encourage pollination, but a lot of times it is just not going to work.
So the short answer is if it is too humid, too hot (above 85 degrees F), or too dry, the plant cannot pollinate itself, so it no longer produces flowers.
It is recommended to continue to keep the plant healthy and change up the environment a bit, either move it to a less hot area, or if you live somewhere humid, you can try to place the plant in the same room as a dehumidifier, and if you live somewhere arid, have a humidifier in the same room as the plant.
Another reason tomatoes won't grow flowers is because the conditions are too good. Maturity occurs when the tomato is stressed (by virtue of a lot of sunlight or dry soil). If the conditions are low stress(consistent moisture and less sunlight), it will take longer to mature and the plant will put all of it's energy towards foliage growth instead of reproduction.
I suggest changing up the environment -- perhaps moving it outside -- to stress it out a little and activate flowering.
Hope this helps and let us know how these suggestions work out for you!