i would start of training my combo's on the bag or pads (standing still)
just till your combo's come natural and not by thinking (cuz then your to late)

then let your partner move while you do your combo's on the pads.
just back and forth, after this let him go in all dirctions. (1 direction during your combo)

when this goes well, let em change direction during the combo, so you can folow the movement when your punching.

after this you do the same, but you dont folow, you cut off the directions (left right) and make him go in a direction you want him to go, so you use your angles.

tell him to trow some punches during and in between your combo's so you stay alert. you can practice your parry/slip and stuff, set up a new combo from your counter.