Looking up the specs, it seems the phone should accept 3.5mm headphone connectors. Working on the assumption that you SHOULD be able to use earphones with a microphone, let us consider the following.
1) Are you using earphones with a 2.5mm jack or a 3.5mm jack? If 2.5mm, then check answers 1a and 1b, if you're using ones with a 3.5mm jack, go to point 2.
1a) If you're using earphones with a 2.5mm jack, you'll need a converter. The converter MUST be a combojack, most 2.5mm to 3.5mm converters will ONLY convert the audio output, and not the microphone.
1b) If you're using earphones with a 2.5mm jack and already have a converter, can you post a picture of the converter as the converter you have may only convert the audio output, and not the microphone (input).
2) If you're using a set of earphones with a 3.5mm jack, have you plugged them in fully? If you're sure they're plugged in correctly, try testing them in another phone to see if they work. If they work in another phone, then your Doogee is faulty, if they don't work in another phone, it could indicate a problem with your earphones.
EDIT: If you have earphones with a 2.5mm jack, then you need a 2.5mm female to 3.5mm male converter which looks like below. If there are any less than 4 metal connectors on the male side, then the microphone will NOT work.