Hey, I've been working on a very similar strategy! You could test out dropping some creatures in favor of token spells to boost the Chimeras.

Spite of Mogis seems relevant.

Here's my deck Really, really wonky burn

Spite of Mogis could be helpful, and I do own 1... Maybe Spite of Mogis instead of Magma Jet? I just don't like the sorcery speed.

Fall of the Hammer instead of Fling

The thing I like about Fling, though, is that it can target an opponent as well as a creature.

I'd definitely play the 4th Lightning Bolt here. The card is just too good.

Electrolyze, Kolaghan's Command, Terminate and Far / Away might be nice.

Spellheart Chimera dies to all of the removal in modern, as far as Breaking / Entering, Thought Scour is basically the surgical way to do nearly the same thing with something more important.. keeping cards in hand. Keeping in the scheme of budget, yea... Gurmag Angler is going be a better Chimera every time.

I really don't see what Gifts Ungiven does except kind of draws you two cards and puts two in the yard at the whim of your opponent. If you do decide to go the Angler route replacing basics with 4-6 copies of the budget fetchlands would be ok. ie - Evolving Wilds, Terramorphic Expanse

Young Pyromancer is an easier to cast Talrand essentially, I always liked the split of 1x Talrand and 2x Y.Pyromancer.

Fetch lands and shock lands will do wonders. This is a three color deck, you kinda need good lands.

Delver of Secrets  ^Flip would do work in this deck. Same with Tasigur, the Golden Fang and Gurmag Angler.

You'll need your full playset of Lightning Bolt. You really need it. Gitaxian Probe and Serum Visions are also very good cards in this type of strategy.

Also, Mana Leak over Rune Snag, and Duress over Despise(Although Thoughtseize and Inquisition of Kozilek are much better).

Finally, maybe add some Cryptic Command? It is one of those game changing spells, and it'd make Epic Experiment a much better card(sad to say, it really isn't that great, just because of the speed of modern, and it's just too slow).