I am being heavily recruited by a former boss to join him at his new company. I am flattered by the attention, but I've only been at my current job for eight months. I don't want to burn a bridge by leaving so soon after my start date. Also, the job my former boss is proposing is a small step up from my current one, but the salary is not much higher.
Since he has been calling me nonstop encouraging me to make the move, can I negotiate a higher salary? Or is that looking a gift horse in the mouth, since he chose to call me and offer me the job?
It's fantastic that your former boss remembers you and thinks highly enough of your work to recruit you into his new organization. You are right to feel flattered.
But however you learn about a new job—from a friend, on a job board, by having a former boss call you, or in some other way—it's always appropriate to negotiate terms that make sense for you. You would be taking a risk by leaving a new job so quickly. (Indeed, there's risk any time you take a new job, just as there's the potential for reward.) Your former boss should offer you something to make that risk worthwhile. That could be more money, a more challenging role, and/or a guarantee—one year or 18 months of salary, say—in case the new company goes under and you're left holding the bag in the form of two back-to-back, short-term jobs on your r´sum´.
Negotiating this offer is not anything like looking a gift horse in the mouth. It's appropriate business practice. Your former boss should appreciate that you are savvy enough to realize what's at stake and that you are entitled to see that your interests are addressed.
Sure, it's an ego boost to get a call from an old boss offering you a job on his team, but it's a job offer like any other. You're a rational businessperson, not a zombie being summoned to join the other zombies on a midnight jaunt. You don't have to follow your former boss's instructions anymore. You, not he, are in the driver's seat now.