How much will connections with the department chair help with grad school acceptance?
You're right, it's sometimes discouraged to get a graduate degree from your alma mater, but it's not as highly discouraged as getting a Ph.D. from the same place you got your master's degree. It really depends a lot on the culture of the department. When faculty are going over your letters of recommendation, test scores, and statement of intent, they're trying to mainly assess:


How likely you are to succeed in the program
How closely your interests align with faculty (i.e Can they help you? Can you help them?)


People can seem amazing on paper and turn out to be a disaster as a graduate student, and vice versa, and faculty will tell you they're taking somewhat of a gamble each year when they admit new students based on application materials alone.

If you've got someone on faculty who can vouch for your intellectual abilities and your fit factor in the department (and you clearly do), then I would say you're very likely to be in a favorable position over other applicants in that department. My department accepted a master's student who had just graduated with their bachelor's from the same department two years in a row.

As far as other programs go, it's extremely beneficial that you have co-authored a published article and would have a letter of rec from a department head. Not a guarantee, of course, but a massive help in any case.