I've had OCBC Frank acct for awhile but decided to transfer everything to my DBS bank acct. Any penalty if my Frank acct is zero? Or should I close down the acct entirely?

If you're above 26, then yes, there's a penalty fee if your balance falls below $1000.

If you're not yet 26, the above is what you'll be mailed with when you're 26. Hence the best is to just close the account to not incurr unnecessary additional costs