Do jigs work well in water below 10 feet deep? What ounce jig do you prefer for these conditions?

Sure they do.  Usually I use 3/8 to 3/4 in football to 3/16 or 1/4 in finesse.  

Any jig will work in either shallow or deep water

Water depth should not control your jigs weight; rate of fall should always control the weight of both jigs and Texas Rigs. A bass can inhale a 1 oz jig long before it ever hits bottom in 10' of water.

Maintain contact with your lure at all times, allow the lure to free-fall unrestricted, but without letting slack form in the line; follow your lures down with your rod tip.

Pay close attention to the depth you're flipping, any sudden change in the amount of line you're using could mean you've been bit. For instance, if you're flipping 6 feet of water and the lure suddenly stops at the 3 depth, it's possible a bass has taken the bait. If you're flipping 3 feet of water and 6 feet of line sinks beneath the mat, chances are good a bass is traveling with the bait. This is extremely true on the initial flip and no line movement maybe noticed.

Strikes will sometimes be so subtle with no line movement that they can go unnoticed if you feel is a spongy sensation, as if the line suddenly got heavy set the hook

Always remember bottom contact is critical!