Your spousal visa has no restrictions or limitations on working, so it should be fine for you to start a UK company.
You will need to register as self-employed with HMRC and sort out all your paperwork for both UK and US taxes etc., but visa-wise, there's no issue.
Something to be aware of though, when it comes to meeting the financial requirement for your next visa, your income can now be considered, but using self-employment income is really tricky because of the sheer number of documents required and the fact that you can only use income from the last full financial year (or last 2 full financial years), and we see more refusals due to issued with self-employment income than any other financial category.
I'm not sure which category you used to meet the financial requirement for your spousal visa, but if there's a chance you will have to use your income to meet the financial requirement and not your spouse's for FLR(M), it's not ideal to be self-employed (we usually advise to only use self-employment income as a last resort, if there is no other possible way for you to meet the financial requirement).
