In a corner, the rounded tip of a Sharpie marker worked well for me. I also have a 4" length of 3/8" o.d. Teflon pipe that's handy on straight corners. The technique I used was to mask off the area on either side of the bead, apply the flox, then remove the masking tape with the excess flox. One final pass with the tool feathered out the edges. Sometimes I would use peel-ply over the joint.
I haven?t worked flox,... but have used the caulk tools. Suspect they would work on small corners. The yellow spreaders mentioned earlier would be needed for larger areas.
I've also taken to using some cheap silicon kitchen spatulas, both Mini and regular sized. I like that they are super flexible and easy to clean and reuse.