Is it a red flag when a guy takes a long time to respond

Pay attention to how the gaps behave over time rather than to any one of them. A guy who usually answers within a few hours and then goes quiet for two days is doing something different from a guy who has always taken a day or so. The first pattern often means something came up or his attention shifted. The second is just how he texts. If you have a read on his usual rhythm from the first few days of talking, use that as the baseline and notice when he moves away from it.

Also check whether the silence is one-sided. If you are the one starting every conversation and he only answers when you do, that tells you more about the level of interest than any amount of waiting will. Notice whether he ever asks you something back, brings up a plan on his own, or remembers a detail from an earlier conversation.

When he does reply after a long gap, the goal is to meet him where he is without over-explaining the delay or making it a topic. Respond to what he actually said, keep your tone the same as before, and give him one easy thing to answer. If you sent a question and he answered it briefly, a good next message builds on his answer rather than reopening the question you already asked.

What to leave out: apologies for being busy, comments about how long it took him, or anything that asks him to justify the gap. Those put him in the position of defending himself, and the conversation stops being about you two. A short, relaxed reply that shows you are still interested without chasing tends to show more about where things stand than an answer that is warm and anxious at the same time.

Timing your follow-up matters as much as the wording. If he goes quiet overnight, do not send anything in the middle of the night that reads as urgent or emotional. Wait until the next day when you are rested and it is easy to keep the tone light. If you have been waiting on him for a reply for a day or two, one gentle follow-up is reasonable, something that gives him an easy out or an easy yes. Something like making a loose plan he can say yes or no to works better than asking 'so what's up with you?'

If you have sent one follow-up and he still has not answered, stop there. Two unanswered messages in a row is a clear answer, and sending a third is mostly about your own discomfort. Put the conversation down, let it sit, and see whether he comes back on his own. If he does, you can decide then whether it is worth continuing.