Transportation from Kyoto to KIX airport

The fastest, easiest route is to grab theJR Trainline’s Haruka Express from Kyoto station to KIX. It runs every half hour. At the train station there will be banks of ticket machines, if you’re feeling all DIY. If not, don’t sweat, standing by will be green vested JR employees just looking for confused or slow ticket purchasers to assist you. You are traveling to the most customer service oriented country in the world.
Otherwise look for the ticket office to hand hold you through the process. If your bags are larger than overhead storage size, remember you’ll need to reserve the back row in a train carriage to be able to store them.
Actually rethink bringing large size luggage to Japan. You’ll regret it.

How do you reserve in advance back row seat to accommodate luggage suitcase larger suitcase and carry-on tote bag?

It has been years, but there was a point to point limousine bus from Kyoto to KIX. It was very convenient and has the advantage of being very easy to bring full size luggage.

I used it many times back in the day.

I second using the JR Haruka Express train, it is clean, fast and efficient. It takes about 80 minutes to go from Osaka to KIX. We had some large luggage with us and had not reserved in advance but there was plenty of room for our luggage.
Have a good trip!

Luggage forwarding in Japan is readily available - it should be relatively easy to research having your large suitcases picked up at your hotel the day before and then retrievable when you reach the airport.

For pricing comparison Japan Transit app is showing the Haruka Express at JPY1860 plus JPY1930 to reserve a seat. Total of JPY3790 for the roughly 90 minute ride. Not sure how much luggage you have but we rode it unreserved with one carry-on and one shoulder bag each without any issues as the train has reasonable luggage space.
And, if you get lucky, you might even get the Hello Kitty Haruka. Didn't matter to us but it was fun when we saw that it would be our ride.

If you are staying at a hotel in Kyoto, I suspect they could offer some choices or advice.
Unlikely you would be the first customer needing to get to the airport.

How do you reserve in advance back row seat to accommodate luggage suitcase larger suitcase and carry-on tote bag?

This requirement only applies to oversize luggage (total dimensions exceeding 160cm) on some routes. Such luggage is also considered oversize by many airlines (like Air France). A 28 inch suitcase, which is already huge for me, is significantly smaller than that.