Really dry and flakey paw pads?

My cat's feel look really dry and flakey. She's always hated it when I touch her feet (to inspect her claws), but now I wonder if it's because they hurt?

Is this because of some diet deficiency? She's on an indoor-only formula, because she's recently become an indoor cat. Or is the flakiness just because she's not running around on dirt and concrete anymore to polish that away? Is there anything I can do? Supplements I can give her, treatments I can do? I'm also on a VERY tight budget, so home remedies would be awesome.

Indoor formulas are not needed for an indoor cat. Look at the ingredients and compare them to the food you were using, in many cases they just decrease the amount of fat slightly and add more grains (carbs) like they do with supposed light formulas.

And her feet are the way they are because she used to be an outdoor cat. Climbing running around on rough surfaces roughens up the pads and can even tear them occasionally.
It's just something that will taken time to heal. As long as there are no cuts or sores, don't worry about it too much.

As for her not liking you handling her paws. Many cats (and even dogs) don't like this. It's something they have to be adjusted to over time. Take your time and slowly get her adjusted to you touching her feet. She not only needs to get used to the feel of someone touching her paws, but needs to learn to trust you doing so.
For all I know, and the way kitties can behave sometimes, some kitties may think we want to chew their paws off.