Yes, walnuts are enough and only a handful per day will provide you with an adequate amount of omega 3's for the day. I would certainly suggest purchasing a small coffee grinder if you can, because freshly ground flax are of the most nutritional value and it's good to get your nutrients from a variety of sources. The whole flax seeds will not offer much in the way of nutrition, although it's fine to eat them that way. It's also important to remember not to heat any of your omega 3's because you will destroy most of the fatty acids.
Keep in mind that poor omega 3 consumption is not only a vegan nutrition concern, but also a concern for omnivores as well. Most people get enough omega 6's but it's important to have a proper balance of omega 3's combined because the two compete for enzymes required to convert small fatty acid chains into longer ones. An imbalance can increase the risk for heat disease, cancer, diabetes, osteoporosis, and multiple immune and inflammatory disorders.
Humans were not always in imbalance, with food processing came the importance of long shelf life and unstable omega 3's were considered undesirable. On the other hand, omega 6 fatty acids rose with the high use of vegetable oils. The proper ratio of omega 6 to omega 3 should be somewhere between 2:1 and 4:1. It should be noted that excessive omega 6 intake, saturated fat, trans fat, low calories and protein, vitamin and mineral deficiencies, alcohol, and smoking can all inhibit proper conversion of small chain fatty acids into the larger ones our bodies require.
The research is still unclear as to whether healthy individuals can convert enough LNA to EPA and DHA (omega 3's), so if you are extremely concerned you may consider a vegan microalgae supplement, since this is our only direct source of DHA which can be converted back to EPA. Supplements can be expensive and scientific research remains unclear, so if you are a healthy individual, you should at least try to be aware of cutting back your omega 6 consumption and increasing your omega 3's.
Omega 6 sources: seeds including sunflower, safflower, hemp, grape, pumpkin and sesame, walnuts, butternuts, corn, soybeans, and their oils.
Omega 3 sources: dark leafy greens, broccoli, seaweed, certain seeds including flax, chia, hemp, and canola, walnuts, butternuts, soybeans, and oils from these foods.
As I stated in the beginning, 1 TBS of freshly ground flax, or 1 handful of walnuts provides us with enough omega 3's daily and these foods are certainly not hard to consume. I mix my ground flax with peanut butter and put it into a sandwich. YUMMY! You can also toss them in a smoothie. Ground walnuts make a perfect cheese substitute especially when mixed with a little nutritional yeast.
Okay, I'm done ranting about omega 3's! A lot of the info I gave was sourced from Becoming Vegan by Vesanto Melina and Brenda Davis. I highly suggest all vegans have a copy on hand as a reference. You can order it on the sidebar.