I replaced the flapper, yet the toilet continues to leak from the tank to
the bowl.

If you didn't use a genuine Kohler part you can't get a good seal. Same with
many other brands. The valve seat itself may be corroded out of round from an
acidic water supply or adding blue goo to the reservoir (see posts in this NG
on that topic).
It's easy to get help from Kohler, Call their customer service at
1-800-456-4537 and get a parts sheet for your Rialto. Order the necessary
pices and install them, and you're likely to be successful. HTH

Joe