I have recently wrestled with chromatic thirds in Chopin's Etude Op 25/6, so I can offer what works for me. Take each voice separately and do the following: 1) Lift tips and follow through to the keybed on each note firmly (can also do rapid long short and short long rhythms too, but, in rhythm work, be sure to release the weight (tension) after playing each long note.) 2) Now play both voices together. Play the thirds in pairs with a down movement of the arm and wrist on the first third and an upward movement of the arm and wrist on the second third in each pair. While doing this, always begin with the arm and wrist up before playing the first third in each pair and, generally, aim the hand in the direction it is going especially on the downbeat eg if RH ascending, aim the third towards the little finger, if RH descending, aim the third towards the thumb, and so on (this movement feels like a slight rotation right or left, depending on the direction of the thirds. 3) For speed, you will need a gentle downward impulse followed by a light (almost weightless) rebound upwards on each beat (and, in many musical contexts, a lateral steering around to the right in RH or left in LH, but there is not much of a sense of this lateral movement in double thirds unless it is a repeating pattern such as a trill or ostinato, etc.) It is essential to have the support of the arm behind each finger in all piano playing, hence item 2) above. The arm will also be diagonal to the keyboard, not at a right angles to it, ie point the arm slightly in the direction of the hand and fingers when playing the thirds (RH ascending, bring elbow into side of body). There must also be a sense of firmness at the fingertips coupled with the bounce and feeling of freedom afterwards on all significant notes (usually the beat notes, but can be every eighth note as in Op10/12, etc). This is typical in all fast playing.
Be patient. Try the above regimen and keep repeating it. Don't play very fast too often or for too long, as this will create unnecessary tension - the enemy of thirds and all fast playing. You'll know when it's working, because the arm will float and you will focus just on the downbeats and the passage will seem effortless.
I hope you can follow this. It is hard to describe technique, because the sensation involved in the process is difficult to convey in words.
Best of luck, mmm151