There are a couple ways to participate in FCBD and I'm not sure which you mean, lol.
Do you mean attending as an artist and doing sketches for people while selling your work?
This is the most common one I see. Each shop (around me at least) brings in 5-10 different artists, gives them a table, and lets them interact with the crowd. You can sell your wares if you have any, but it's also encouraged to do free little sketches for people (or sometimes they might still have you charge, but it's for charity). Gives the kiddos a cool souvenir, you sell a couple things, and you can connect with random comic readers in your city. ** SIDE NOTE: A lot of artists I know that do FCBD only offer free sketches without selling anything. That's okay too if you don't have merch! I recommend at least having business cards and a portfolio for people to flip through though.
If you are selling, don't expect to sell a ton. It's more a way to have fun in the community and network. I sold couple books here and there and some small merch. The artist next to me though always did really well with his monster stickers. I think those and buttons are a good idea for a $1-3 item that parents feel comfortable paying for randomly, since most of the people coming in for FCBD are families.
You'll run into people asking if the stuff at your booth is free, though, since the pretense of the day itself if getting something for free. So I think having SOMETHING small available to give out (whether that's a zine with samples of your work, A postcard with art on one side and your info on the other, or a sketch) is a good idea.
In general I always suggest getting to know your local artist/comic scene, but if you weren't sure how to go about it, this is a good way to break the ice. Go to a few comic shops and ask if they participate in FCBD (not all of them do), then see if they do anything with local artists. Doesn't hurt to ask!
Do you mean giving a comic shop some books to pass out for FCBD?
I've done this too, but only under very specific circumstances because printing is expensive. I did it because:
1- I already had a good, long lasting relationship with the comic shop I brought it up to
2- My artwork is professional grade, so it didn't look out of place
3- I had totally overshot on reprinting my issue #1, thinking it would still sell after I printed a compilation. I was wrong.
I had like 500 of these things sitting in my basement. I could either let them rot there, recycle them, or list them as a promotional expense and give them away for free for marketing. I decided on the latter. I kept some to still sell at cons but the rest I tried to move in as much bulk as possible (I'm still working on it a year later, but I've finally moved like 400 of them, yay!).
If I DIDN'T have those excess books, I wouldn't have bothered. FCBD is cheap for big publishers and a good marketing investment because they print thousands to distribute across stores all over the country. Us little guys going through the trouble of printing our work to give it away for free is a bad money sink. There are other, better ways to promote ourselves. General rule of thumb is, if you're getting your content printed professionally, you best be selling it.
If you're making a handful of zines yourself with printer paper and samples that's one thing, and those can be given away for free if you want. Buuut I don't think most shops would be okay placing those next to all the other FCBD stuff... I guess you could always ask, but you'd need to assemble like 50-100 of them.
OR, do you simply mean that you want to offer your own comics in your own online store for free for a day?
(Added this third option after rereading OP and figured this might actually be what you're talking about. I took your question as about the EVENT in stores initially)
If you want to do this, you could. I would discount it on your store or advertise a coupon code that makes it free for one day only. You could spread it around on social media and tag it as #FCBD. I don't know if you'll get as much traction since it's not community based like the actual event, but it might net you some new fans. Encourage people to share/retweet/whatever the post so it gets around.
