If a LLC does a 1031 exchange, do I need to report it on Form 8824 in my personal tax 1040?

Yes.  

Entering a like-kind or Section 1031 exchange (Form 8824 generated):

1. With your return open in TurboTax, search for like kind (2 words, no dash) and select the Jump to link at the top of your search results
2. This will take you to Any Other Property Sales?  screen. Select Any additional like-kind exchanges(section 1031) and select Continue
3. On the next screen, select Yes and proceed through the interview questions. We'll fill out Form 8824 for you

Please see TurboTax Help FAQ for additional information: Where do I enter a like-kind or Section 1031 exchange (Form 8824)?

The response by @TomK2023 assumes that your LLC is a single member LLC and is under the provisions of the default treatment being a disregarded entity: since you are asking from TT online version.

If this LLC made any other type of election, other than the default, then the response will be different.

My CPA says that my LLC tax return has reported the 1031 exchange already. But I am also hearing that I need to file Form 8824 and hence I am confused.  Do I really need to file Form 8824 if the LLC has reported the exchange and the new home and Capital gains is inside the LLC's bounded tax context? 

Before we can answer this question, we'll need to clarify what kind of business structure do you have?

My LLC is associated with just the rental property and both my spouse and I are equal share holders of the LLC. 

Thanks for the extra information regarding your spouse and LLC. Since you have a CPA doing your LLC tax return, I believe you are in a partnership with your spouse and not in a community property state. You would not need to report the 1031 exchange a second time.

It should only be reported once, by the entity. You would enter the k-1 information from the partnership but not the 8824 again.