The "standard" fingering for scales in thirds, right hand ascending, is groups of 31 42 31 42 etc, plus the occasional 31 42 53 31 42 etc to keep your thumb off the black keys as much as possible. (Be thankful your arrangement only has one sharp in the key signature, not four or five!)
I gave that ascending not descending because for me, it seems easier to figure out how to play this completely legato at a slow tempo (except for the 53 to 31 transitions) ascending rather than descending, though once you see what the movement needs to be, it works in both directions. To get from 42 to 31, your thumb goes under the 2, and your fourth finger goes over the 3. Imagine you are a crab walking sideways along the keyboard, or a spider "feeling" with your fourth finger for the next note to play above the third finger.
Descending, the 2 goes over the thumb, and the 4 goes under the 3.
Start by practising this very slowly - 40 notes (not beats!) per minute is plenty fast enough till you start to get the feel of the 42-to-31 transitions. If you try to run before you can walk, your fingers will literally "fall over" each other.
A preparatory exercise is to hold a long note (say G) with your thumb (just to "anchor" your hand and take the weight of your arm), then play B C B C B C etc, legato, but with the fourth finger on B and the third finger on C - the opposite way round from how you would normally finger it. Turn your hand sideways so your fingers point to the right, to make it easier.