If one of my toons had the Flash boots or the Gloves of Grappling, is that what they would be called in my style tab? "Flash Boots" and "Gloves of Grappling"?
No. I believe the style for the Gloves of Clinging is Bat Gauntlet or something like that. Can't remember the name of the style for the SS boots, but it's definitely not Flash Boots. Edit: the style for the SS boots is Journeyman.
Can any one help me I am looking for a style where the hands look like they are surrounded in electricity
There might be a couple of options for that. First, if you use Hand Blasters as a weapon, you might want to look into the Voltaic Weapon pack on the Marketplace. The Voltaic HB style more or less covers your characters hands in a glove of electricity. Plus there should be an option when purchasing that to get the alternative version where you can see your character's hands through the electricity (the original version made your character's hands kinda disappear lol). The other option would be through the Quark vendor. You can get modular versions of the powerset auras that came out a while ago, so you'll want to look for the Concentrated Power Set Aura box. From there, you'll want to choose the Sparking Aura and choose the "hands" version. EDIT: The Sparking Aura-Hands and Voltaic Blasters HB style can be used at the same time, so you can get a really interesting look if you use both of them.