FKG's a bit like Aigis in that you don't really expect to get your game currency through login bonus/dailies, but instead through events. But FKG's more generous in that regard as it's very consistent in effectively offering 8 gems per week through the new event, plus 1 gem per week through reprints. And with the way they design event maps now, things are almost entirely a question of whether you have the stats. The stripping away of required interaction has its own sets of pros/cons, of course. But anyway, after a certain point, the event gems are as easily acquired as another game's dailies.
So it effectively alternates between 5 and 6 weeks between each 10+1 draw as far as reliable gem gains go.

As far as a 10 draw in Kamihime goes... 840 jewels over a 12 day cycle? 36 days (3 full cycles) gets you to 2520 jewels. 480 jewels left before you hit 3k... that's 10 days worth of dailies, but within those 10 days, you should gain 140 jewels from login bonus (I don't remember which days). It should take no more than 45 days to generate 3k jewels via login/dailies.
Event gains would be uneven, as it would vary depending on the event type. Also, have we settled on 2 days break between events? Eh, I guess for back of the envelope style estimates, we can go with assuming an event every 10 days. Advents are 50/100/150/200 jewels each. Raids are 200+ each (wait, do the story missions in raid event give jewels too?). Union events.... vary depending on union. For myself, I'd probably estimate 200 jewels per event to be safe (disregarding whatever jewels I roll through raid gacha). There's maybe about 3.5 events over 3 cycles; definitely at least 1 event per 12 day cycle. You can underestimate at 3 events over 36 days and still probably come out with a 10 draw worth of jewels in that time period. So, ~5 weeks for every 10 draw is my estimate, without accounting for random special bonuses.