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The most important thing to know for August 1st is that if you have control over your private keys, you will get BCC. If your storing money on an exchange, you lose this control - at which point its up to the decision of the exchange if you get BCC or not. If your storing BTC on an online wallet like Blockchain.info then you do not control your private keys.

Would something like Coinomi give us control over our private keys, allowing us to grab some BCC?

Coinigy is an interface, not a wallet. Coinigy has no access to your private keys (or public keys for that matter). The private keys are being stored by your wallet and /or exchange. Some exchanges have refused to support bcc because it is a maverick coin that is bad for the cryptocurrency image and ecosystem, I agree with that sentiment.

A month late, I know, but I believe @cmd-space meant Coinomi, the multi-coin HD wallet, not the charting/trading platform