Re: Flex time goes out over time...

That's not a great value for a loop, and especially not good with the dot at the end. I'll explain...
The 1 indicates that your loop is 4 bars and 1 tick in length, so there's no way that'll loop properly. The loop will likely start to sound out of time after just a few repeats. Now, the dot is another story... it means that the length of the loop is 4 beats, 1 tick, and some number of samples long in length. Normally you should be able to cut a loop exactly on a beat and not have any fractional bits left over. But due to what I consider to be a bug in Logic (since Logic 8), sometimes cutting a region on a beat results in some fractional amount in addition to the length you expected. When this problem occurs, the loop length will appear as an 'even' length (like 4 0 0 0) but with a dot at the end. (I can't account for why your loop has the extra tick in it, though).
So the best thing would be to try and trim that loop so that it's exactly 4 beats long, i.e., 4 0 0 0, no dot at the end. Unfortunately, sometimes it's not possible to get rid of the dot! Suggest you try the following:
Approach #1: use the scissor tool to trim the length down to exactly 4 measures and delete the leftover bit
Approach #2: set the playhead to be exactly at the 4 measure mark and use the key command called "Set Region/Event/Marquee End to Playhead Position" (that's a mouthful)! Of course you want to be sure that your region starts exactly on a beat to begin with.
If neither of those results in a region that's exactly 4 measures long, bounce the "long" region (use Bounce in Place if you want). Then try trimming that region to be exactly 4 measures.
Let us know how you make out.