Where I work, the other four members of my department always arrive at random times, usually latter than when they are expected. It is not uncommon for two of them to arrive around 11am. I know it's none of my business why they are late so I'm wondering if would be an appropriate request to ask them to let me know around what time they plan to be in the next day? They also leave at random times. Can I ask what time they are leaving? I think this would impact my work in a positive way because I could make sure to talk to them before they left if I have any questions or concerns. I'm worried that I will offend them as they get super defensive really quickly so I need to word it carefully.
In business and in life, it is better to ask directly for what you need. You need to meet with your colleagues. Instead of asking them when they plan to arrive or depart, ask them if they can meet with you: "Alice, can you meet with me this afternoon? I have questions about the transmogrifier."
There are a few ways to approach this.
First, companies with more flexible hours sometimes have "core hours" - perhaps 10am-2pm - where employees need to be on-site, for purposes of scheduling meetings, etc. Find out if your company has these (sounds like "no" or at least they are not enforced).
Second, try scheduling an actual meeting. If you need to talk something over, add it as a meeting on calendars. Then, if they are gone, you have a more natural way to bring this up. "Hey, we had a meeting at 10am, I know you generally come in between 9am and 11am, will 10am work in the future? What time is better?" instead of coming across as a creeper.
Third, does anyone on your team work remotely? Perhaps they work from home some, etc.
I would definitely NOT recommend bringing this up without a specific instance, though, as it would be a bit weird to me. I come in at 8am (most others here start at 7am) and it would be weird if someone asked me, "why do you come in at 8 instead of 7" - and that's just one hour difference.
There is one situation where asking about co-workers work schedule is important. When the team is responsible for staffing the office for the entire workday. The people that arrive early like to know when the rest of the team will arrive so that calls/requests can be handled properly. I have been in this situation and I don't like having to keep telling people I have no idea when Joe will arrive. The people that stay past dinner time want to know when the others are leaving.
If their overly inconsistent hours impact the office performance directly then you can ask, but if the only thing that is impacted is the ability to ask a question face-to-face then drop the subject.
If the company allows for liberal flex time, then you are better off just focusing your efforts on your specific tasks. From a professional point of view, if the lack of scheduled hours begins to create dissension between your department and other departments in the company, your manager will be informed and it will be up to him/her to adjust the policies accordingly, if he/she chooses to do so. From your explanation, you are not the manager, so therefore, your focus should remain on completing your tasks and not trying to take responsibility for anyone else's tasks or lack of responsiveness.
From a personal point of view, it could reflect negatively on you in a number of ways. From the perspective of your manager, you could be seen as someone who isn't a team player and is more focused on their ambitions than the overall success of the department as a whole. You also may be perceived as lacking the objectivity to fit into the cultural makeup of the organization, which may make it more difficult for you to advance to a leadership position. From the perspective of your coworkers, simply stated, no one likes a tattletale. You don't know what arrangements they have made with their manager to have the flex time they have, and it's really not any of your business. They are not keeping you from getting your work done...they are only keeping you from getting your work done in a manner that's acceptable to you. When it all boils down, if your manager doesn't have an issue with the quality of your work, then why create a problem where none currently exists?
Relax. Do your job. It is possible that you may be modeling the future behavior of the department...they just don't know it yet. Let things happen, and worry about those things you actually have control over.
Unless they are direct reports, then you don't have the right to ask this, and it could be taken as a negative response.
They may also have agreed those start/stop times with the manager, which you would not be made privvy to (eg. Pick up kids, hospital appointments).
If it is impacting the job, then mention it to the manager.
If your reason is actually to ask a question, then use email or some IM that tracks when you asked/answered. That way if the question/response delay impacted the project you have a log related to that later on.
If your questions are making them defensive, possibly they are not understanding why you are asking, and are assuming you are just being nosy or disruptive. Best would be to pay attention and wait for a specific instance where your lack of knowledge produced a bad result - maybe a missed opportunity, or a incompleted phone call, or a call-back to a manager.
At that point, you could say, "Bruno, if I had known you would be here at 12:30, we could have scheduled the conference call for 1. Would it be better to call you at home when you're not here to find out when you will be in, or to assume you will always be in by 2?"
The fact that they are defensive, rather than co-operative, makes me think there is something else going on here that needs more explanation, or exploration (depending upon whether you know what it is, or not).
I've worked at many jobs where people had a lot of autonomy, and I've never seen a situation where someone was unwilling to be communicative, if it was being done in a constructive manner.