I prefer tea to coffee.
I drink tea at least three times a day.
Sometimes I drink coffee but it gives me a headache.
I like coffee, so this is kind of a problem.

I've heard good things about drinking tea, like that black tea will prevent the flu.
The flu is going around Japan at the moment.

So drink black tea, everyone (and do not take milk)! 

Well done!

Just a few changes to make it sound more natural.

I prefer to tea to coffee.

I prefer tea to coffee.

I drink tea three times in a day at least.

I drink tea at least three times a day. 

I sometimes drink a coffee but it gives me a headache.

Sometimes I drink coffee, but it gives me a headache.

I like coffee, so it's kind of an obstruction.

I like coffee, so it's kind of troublesome.

I've heard the good thing of drinking tea.

I've heard benefits of drinking tea.

Black tea will prevent the flu.

Black tea prevents the flu.

The flu is going around in Japan.

Drink black tea, everyone! (do not take milk)

Drink black tea, everyone! (Do not add milk)