This is not an easy question at all. I am not sure you will find what you'd like, as sewing (and anything remotely related) has lost a lot of popularity in the last decades. I like to crochet and knit and there are 2 shops in Florence where I can find yarn -- over the years, several others I knew have closed down.
I had trouble also knowing where to buy thread and needles - until I found at "mercerie" are the stores that carry them. Through the years, these stores have also stopped selling these types of items and sell other items, such as pjs and home linens, where they know they'll have more customers.
What I have seen are made in China cheap travel kits, not at all what I think you have in mind.
Having said this, in Florence, for scissors you'd head to a "cutting" store, where they specialize in sharp objects, in this case, the most common are knives. These are the stores that also have scissors of all types.
In the center, this one is more famous: Coltelleria Bianda on Via della Vigna Nuova 86R - http://www.coltelleriabianda.it/ It is where the original owener of Colterria Donnini (when it was owned by Galli) trained as an apprentice.
It is likely you will find a very plain embroidery-type of scissors.
If you really want something special and possibly inlaid, then you have to head north out of Florence to Scarperia in the Mugello, a town known worldwide for its artisan trade in this sector. I've seen beautiful items there, but I am not sure whether you'll also be able to find a "kit" with thimble or thread.
In any case, keep your eyes open just in case -- there are a few boutique shops between Piazza Duomo and Ponte Vecchio (and on Via Tornabuoni) that specialize in embroidered and hand-crafted clothing items, I've never entered and asked but wonder if they have these sort of items in their store or at least point you in the right direction? It might help to ask artisans where they get their own tools!