Will I still get flagged for missing my height and weight, even if I pass my PT test?

Soldiers are required to conduct HT/WT every 6 months at a minimum, but the Commander of a unit can order Soldiers at any time to conduct HT/WT. The only time you do not have to get HT/WT is if you score 540+ (min 80 points in each event). Your 538 means you get HT/WT and taped.

If you fail the tape, then yes you will be flagged. If you purposefully try and skip the HT/WT, then yes you could be flagged because you could be facing some sort of administrative action.....like an Article 15 for disobeying a direct/lawful order.

Yes - or at least this was the case when I was in. Height/weight requirements are/were independent of your physical fitness.

Everyone is required to be within standards. Height and weight is a requirement with exceptions. As MSgt Livingston said if you have 540 plus as your score you get a pass. You didn't. If you fail height and weight the tape is an exception to help you out. If you fail height/weight and also fail tape then anyone would get flagged. If you are going to school you will need to have this under control because I assume they will test you at school and do height/weight while there.

First, it is not "for no reason", it is required by reg every six months:
4 AR 600–9 • 16 July 2019
3 – 2. Standard
a. Soldiers are required to meet the prescribed body fat standard, as indicated in appendix B. Soldiers will be screened
every 6 months, at a minimum, to ensure compliance with this regulation
https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/ARN7779_AR600-9_FINAL.pdf

Second, if you are worried about making tape, you have several options:
1. lose enough weight to make your screening weight every time
2. lose enough weight to pass tape every time
3. always score 540 or better with at least 80 points in each event on the ACFT so that you do not have to tape if you are over screening weight. if you are flagged and on ABCP, you can also complete a new ACFT, scoring 540 with 80 in each category to get off ABCP and remove the flag:
https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN37812-ARMY_DIR_2023-08-000-WEB-1.pdf

So yes, if you fail the tape you will be flagged and ineligible for schools. You can either lose the weight, inches, or a complete new, higher ACFT score to lift that flag.