Traveling within US with pending Visa U [duplicate]

I assume that "pending U visa" means that you have applied for a change of nonimmigrant status to U status, and that your application has not yet been decided. If that is incorrect, please leave a comment on this answer to explain.

To fly domestically in the US, you must prove your identity. Your foreign passport, if you have one, is the best way to do that. The full list is on the TSA's identification page.

The TSA will not pay any attention to your immigration status. However, there is a small chance that you will encounter US Border Patrol officers at the TSA checkpoint. If you do, they will want evidence that your presence in the US is compliant with US immigration law. If that happens, you can show them the receipt for your pending application. If your prior nonimmigrant status is still valid, you should also show them any evidence related to that. The specific evidence depends on the status in question.

For this answer, I assume that you have valid ID (a foreign passport, for example) but do not currently have a valid Visa to enter the US (since it's pending).

As the linked answers explain in more detail, you only need a visa to enter the US, not to fly domestically within the country. As long as you have valid ID (See the answer by @phoog for a list of valid ID), you shouldn't have a problem flying within the US regardless of your visa status.

Can I travel when US visa extension is pending?

Expired visa, can I still fly inside US without risk?