Kinesthetic learners can be quite challenging to teach with traditional techniques including multiplication flash cards. It is important to teach your child using the methods which they excel in. Check out the brain gym techniques to help your child in all areas of learning. Also look at Multiplication Education for help to learn the multiplication tables.
Put small things - like dried beans - in piles according to the table you're teaching. 3,6,9,12,15, 18 etc. This will take some work and some clean up. Use real things as much as possible to teach math facts.
My son is also a third grader who shows strong kinesthetic abilities.
If your child is responsive to music or video; have you tried math to music. You can play CD's or even have him/her stand while watching youtube videos that have song or dance to math.
I have heard some negatives in regards to Flocabulary, however my kinesthetic(and music lover child) responds very well to learning vocabulary when set to music or singing.
I hope this helps :)