Grad Application: Research Experience without Letter of Recommendation
First, note that it is only a red flag if you are omitting the most recent or only research experience.  You are generally only required to get a few letters of recommendation. If you need N recommendations, and have a sufficient set of strong and recent recommenders, then there is simply no reason to get additional weak recommendations beyond your N strongest.

Omitting from your CV, however, is probably a bad idea, because it can be considered dishonest.  In my experience, a full CV should include both your triumphs and your sins, and hiding your sins will only increase your trouble when they come out at a later time.

If you don't have other more recent research experience, but you didn't completely burn your bridges, you might approach this by having a very blunt conversation with your former advisor.  Lay out your concerns like you have here and ask what the professor would suggest is the best path forward.  They may be willing to write you a very neutral letter, e.g.:


  X was a member of my group for a brief time.  It was not a good fit, but I believe they have the potential to do well elsewhere.


Then you can lean on the strength of your other letters be essentially evaluated as having not done research.

If you've really angered the professor, though, and have no other research experience, then it may be the case that the only good way to address this is to get some more research experience.