The farthest upgrade you can do wtih your PBook is Leopard v10.5. iCloud requires that you have a Mac running Lion v10.7.2.
The downside to upgrading to Lion would be the price. Try Amazon.com
Make sure your Mac meets Leopard's requirements > Requirements for Mac OS X v10.5
And even with having Leopard installed, Safari alone can only be updated to 5.0.6. Farthest you can update Safari for Tiger v10.4 is 4.1.3.
Flash would be the same that you have installed with Tiger. Flash 10.0 r45.
If you decide to upgrade to OS X Leopard 10.5, Apple no longer sells it. In the used market, be aware that any gray-faced OS X Leopard disk you buy won't work on your PowerBook, as they are locked to the system type they were delivered with, and 10.5 Leopard was never delivered with a PowerBook. You'll want to buy a black-faced retail copy. Here's one source for unopened Apple software.
This will solve the Flash problem.
Flash Player version 10.1.102.64 is the last version available to PPC Mac users. However, this Flash version won't work for many videos on Facebook, YouTube and other sites. Adobe's latest version, 10.2.x or later, is only for Intel Macs. Adobe will not provide a newer Flash version for PPC Macs.
The message requesting that you download Adobe Flash Player takes you to Flash Player requiring an Intel processor. Doesn't work on a PowerPC processor. I found a hack, installed it & it works with Firefox, TenFourFox & Safari.
Download this http://www.steelbin.com/FPforFBPPC.zip to your desktop, unzip it, and replace the current Flash Player plug-in which is in your main/Library/Internet Plug-Ins folder, (not the user Library). Save the old one just in case this one doesn't work.
Hack Allows PowerPC Macs to Access Flash 11 Content
Mac OS X 10.5 Leopard installation system requirements
Leopard is no longer available at the Apple Store but may be available by calling Apple Phone Sales @ 1-800-MY-APPLE (1-800-692-7753).
If you can't obtain a retail install DVD from Apple, look on eBay or Google the installer part numbers to possibly find at an on-line store. Here's what to look for:
MB427Z/A Leopard 10.5.1 install DVD
MB576Z/A Leopard 10.5.4 install DVD
MB021Z/A Leopard 10.5.6 install DVD (single user)
MB022Z/A Leopard 10.5.6 install DVD (5-user family pack)
Installing Mac OS X 10.5 Leopard
Mac OS X 10.5 Leopard Installation and Setup Guide
After you install the base 10.5, download & install the 10.5.8 combo update at http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update
The DVD should look like this
Caution - Leopard does not support classic mode. So, if you currently open OS 9 apps in classic mode, you won't be able to do this if you upgrade to Leopard.