I have also the same issue. I would like to have membership shield of each member showing in Profile under General info section.
I got given instructions from Anton, but it is too abstract for me. I would probably need more detailed instruction.
Blocks are located in sys_page_compose table. You may do changes in showBlockPFBlock function in templatesbasescriptsBxBaseProfileView.php file. Id info block is 80.
Info about membership level you may get in inc/membership_levels.inc.php file. Here you may get current membership level for members.
I am sure there is plenty of experienced programmers here for which this would be a piece of cake.
Thanks.