how to incorporate a family hankerchief

That's a tricky one. All of the ideas I came up with involve damaging the hanky (sewing it into something) and it sounds like it's too important to damage.

I friend made my flowers for me - she was able to wrap my grandmothers scarf inside the bouquet through the flowers - it was hidden but I knew it was there. If its small, you could pin it inside your dress at the bottom. That way its not uncomfortable. I also had my grandfathers' handkerchief (is was small) I carried it in my hand through the entire ceremony (my Grandfather is deceased to that was my way of having him walk me down the aisle). I hope this helps.

If you don't want to pin it on the inside of the dress, could you wrap both around the bouquet? They both may not be seen, but you know they are there.

Can FH use it as a pocket square? You could also lay your accessories on it for pics. Depending on what you're doing with the rings you can put it on a tray/box or pin it on the pillow & put the rings on the hanky. You can also ask the florist if she can use it to wrap the flowers instead or with ribbon & then you can hang your other stuff on top of that. Or just hold it during the ceremony to dry any happy tears & put it in your purse after.

I am going to carry a handkerchief that belonged to my grandma with my bouquet and use it if needed.

You can put it in the flower girl basket or have FH carry it on him.

You could sew it onto the inside of your dress. (pic for reference)

I like the idea of the florist putting it in the bouquet but I won't be able to get it to the florist beforehand. Do you think I can just fold it up and stuff it in?.... without damaging flowers or risking it falling out?

I also like having FH carry it and give it to me to dry tears but would it be ruining it to get makeup on it?