Is not including a letter of recommendation from all of my research advisors in grad school applications an automatic red flag?
It is not a requirement that you include letters from every research advisor you've ever worked with as part of your graduate application. Since you already have letters from multiple research advisors, you can choose your third letter accordingly. If you believe the letter from your academic advisor is more helpful to you, then you should continue to use that letter. For example, your third advisor could more helpfully comment on your teaching abilities, if that is something you feel is important in your application.