No, you can't run flash and it's probably because of the hardware restraints of the handset (I posted some of my findings about the p350 on the previous thread, but as a newbie I can't post links yet).
Nevertheless, you can watch youtube videos and play some pretty heavy games on it. It's a simple, budget handset and I find it somewhat *braver* than other budget Androids I saw in the same category. Don't give up on it.
"1 - Battery life: 5 to 6 hours with 3G, Wifi, Bluetooth or GPS always turned on. I managed to extend battery duration using the Power Control widget to disable all this services when I'm not using them. I also rooted the beast using gingerbreak.rar following a tip on this forum and managed to install the SetCPU app, which can under-clock the handset to 122Mhz when the phone is idle. It's useful and spares a lot of battery. Managing the background apps and wireless connections as well as underclocking the handset makes battery life improve to something like 6 to 7 days.
2 - Performance: Avoid, if you can, the G+ client (I can't). I love Google Plus, but the client for Android looks bloated - at least for this handset. It clogs memory, sucks up CPU cycles and makes the overall experience miserable every time it's running. The BBC News and Economist apps were also bad so I uninstalled them right away. Bloated apps make the P-350 very unhappy.
3 - 3G: Although it's fast and works splendidly on the p-350, my data plan cap sucks, so I'm using 2G and sparing battery power and a few bucks. The WiFi feature is very decent, too, and I managed to achieve 7Mbps downloads measured with the Speed Test app.
4 - Apps: The Advanced task killer app helped me to unload background apps like G+, music, or any other I'm not using for the moment. As for the apps, Twitter, Facebook, World Newspapers, Opera, RT, RealCalc, AdobeReader, VNC, ASTRO, ES Task Manager, Landroid, Photoshop Express, Picasa Tool, Goodreads, Chrome to Phone, Barcode Scanner and Dropbox apps, among others, are all ok and light enough to provide a positive experience on the handset. Fifa 10, Pool Master, Quake, AngryBirds, PaperToss also ran beautifully.
5 - Games: Gaming is decent provided you disable everything (WiFi, auto-sync, GPS, bluetooth) and make a preemptive cleaning on the background running apps.
6 - Voice: For a LG , the phone system is pretty good. My kid used to have another - non-Android - LG handset and call/voice quality sucked bad.
I just keep in mind this phone CPU makes 600 bogomips, measured by SetCPU, and this is the same what a AMD K6 from years ago did (as opposed to the 3000 bogomips a Galaxy SII provides, which is comparable to a Pentium 4 1500Mhz), so I had to barebone the OS to the maximum in order to squeeze the best performance from it."